A comprehensive guide to circle geometry covering essential formulas, properties,... Show more
Earth and Space ScienceSign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
738
•
Feb 9, 2026
•
Circles Unit Geometry Reference Sheet - Free PDF Download
Tristan Zoarob
@zerakat
1 / 7
Page 1: Essential Circle Formulas
This page introduces the fundamental formulas for working with circles, serving as a circle theorems booklet introduction. The page presents basic circle measurements and terminology with clear diagrams.
Definition: The diameter (d) is twice the radius (r), expressed as d = 2r
Vocabulary: Key terms introduced include tangent, point of tangency, diameter, circumference, radius, chord, center, segment, sector, secant, and arc
Highlight: Essential formulas covered include:
- Area: A = πr²
- Circumference: C = 2πr
- Radius calculations from both area and circumference
Page 2: Circle Angle Properties
This page explores the relationships between angles in circles, forming a crucial part of circle theorem proofs pdf. The content focuses on inscribed angles and their properties.
Definition: An inscribed angle is an angle with its vertex on the circle's circumference and sides forming chords
Example: When an inscribed angle intercepts a diameter, it forms a right angle (90°)
Highlight: Key properties include:
- Central angles measure the same as their intercepted arcs
- Inscribed angles measure half of their intercepted arcs
- Opposite angles in inscribed quadrilaterals are supplementary (sum to 180°)
Page 3: Tangent Properties
This section details the properties of tangent lines and their relationships to circles, essential for understanding properties of circle class 10.
Definition: A tangent line touches the circle at exactly one point (point of tangency)
Highlight: Three main properties are covered:
- Congruent tangent segments from external points
- Perpendicularity of tangent lines to radii
- Properties of circumscribed polygons
Page 4: Intersecting Lines
This page examines the relationships formed when lines intersect within and on circles, crucial for igcse circle theorems notes.
Vocabulary: Special angle relationships are formed when chords, secants, and tangents intersect
Example: Inside the circle, angles are measured using the formula: ½
Highlight: Different intersection scenarios are presented with their corresponding angle measure relationships
Page 5: External Intersections
This section focuses on angles formed by lines intersecting outside the circle, expanding on properties of circle formula.
Example: For two secants intersecting outside the circle, the angle measure is calculated using specific arc measures
Highlight: Three scenarios are covered:
- Two secants
- Two tangents
- One secant and one tangent
Page 6: Segment Length Relationships
This page details the relationships between segment lengths when lines intersect, essential for circle properties and formulas pdf.
Definition: When chords or secants intersect, their segments form proportional relationships
Example: For intersecting chords: a = c
Page 7: Circle Equations
The final page covers the algebraic representation of circles, completing the circles unit geometry reference sheet pdf.
Definition: Standard form: (x − h)² + (y − k)² = r² General form: Ax² + By² + Cx + Dy + E = 0
Example: Detailed step-by-step conversion from general to standard form
Highlight: The process includes completing the square for both x and y terms to achieve standard form
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content: External Segment
Most popular content in Geometry
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Circles Unit Geometry Reference Sheet - Free PDF Download
Tristan Zoarob
@zerakat
A comprehensive guide to circle geometry covering essential formulas, properties, and theorems in circle properties and formulas pdf. This reference material includes detailed explanations of circle parts, angles, intersecting lines, and circle equations, making it an invaluable circles unit... Show more
Page 1: Essential Circle Formulas
This page introduces the fundamental formulas for working with circles, serving as a circle theorems booklet introduction. The page presents basic circle measurements and terminology with clear diagrams.
Definition: The diameter (d) is twice the radius (r), expressed as d = 2r
Vocabulary: Key terms introduced include tangent, point of tangency, diameter, circumference, radius, chord, center, segment, sector, secant, and arc
Highlight: Essential formulas covered include:
- Area: A = πr²
- Circumference: C = 2πr
- Radius calculations from both area and circumference
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 2: Circle Angle Properties
This page explores the relationships between angles in circles, forming a crucial part of circle theorem proofs pdf. The content focuses on inscribed angles and their properties.
Definition: An inscribed angle is an angle with its vertex on the circle's circumference and sides forming chords
Example: When an inscribed angle intercepts a diameter, it forms a right angle (90°)
Highlight: Key properties include:
- Central angles measure the same as their intercepted arcs
- Inscribed angles measure half of their intercepted arcs
- Opposite angles in inscribed quadrilaterals are supplementary (sum to 180°)
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 3: Tangent Properties
This section details the properties of tangent lines and their relationships to circles, essential for understanding properties of circle class 10.
Definition: A tangent line touches the circle at exactly one point (point of tangency)
Highlight: Three main properties are covered:
- Congruent tangent segments from external points
- Perpendicularity of tangent lines to radii
- Properties of circumscribed polygons
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 4: Intersecting Lines
This page examines the relationships formed when lines intersect within and on circles, crucial for igcse circle theorems notes.
Vocabulary: Special angle relationships are formed when chords, secants, and tangents intersect
Example: Inside the circle, angles are measured using the formula: ½
Highlight: Different intersection scenarios are presented with their corresponding angle measure relationships
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 5: External Intersections
This section focuses on angles formed by lines intersecting outside the circle, expanding on properties of circle formula.
Example: For two secants intersecting outside the circle, the angle measure is calculated using specific arc measures
Highlight: Three scenarios are covered:
- Two secants
- Two tangents
- One secant and one tangent
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 6: Segment Length Relationships
This page details the relationships between segment lengths when lines intersect, essential for circle properties and formulas pdf.
Definition: When chords or secants intersect, their segments form proportional relationships
Example: For intersecting chords: a = c
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Page 7: Circle Equations
The final page covers the algebraic representation of circles, completing the circles unit geometry reference sheet pdf.
Definition: Standard form: (x − h)² + (y − k)² = r² General form: Ax² + By² + Cx + Dy + E = 0
Example: Detailed step-by-step conversion from general to standard form
Highlight: The process includes completing the square for both x and y terms to achieve standard form
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
45
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Practice Test ✓ Essay Outlines
Practice Test
Quiz
Flashcards
Essay
Similar Content
Tangent Lines Homework (unit 10:circles)
Unit 10-Circles
GeometryGEOMETRY UNIT 10 POSTULATES AND THEOREMS
***there may be grammatical or spelling errors and many abbreviations as these were originally just for me; it is not guaranteed to be 100% accurate***
Geometry9th
Circles
Segment relationships
GeometryTangent and Secant Theorems
This page talks about the two secant segments theorem, the tangent secant segment theorem, and how to solve problems for each.
GeometryGeometry Unit 10 Lesson 1
Geometry Unit 10 lesson; Tangents
Geometry9th
Essential Circle Theorems
Explore the fundamental circle theorems, including the alternate segment theorem, properties of cyclic quadrilaterals, and relationships between angles in circles. This summary covers key concepts such as inscribed angles, central angles, and tangent properties, providing a clear understanding for students preparing for exams.
Maths10
Most popular content: External Segment
Most popular content in Geometry
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user