The angle in a semi-circle is 90°. This means that if we draw a line from one end of the diameter to the other, the angle where it meets the circumference will always be 90°.
Cyclic Quadrilateral Properties
In a cyclic quadrilateral, opposite angles add up to 180°. This is an important property to remember when dealing with cyclic quadrilaterals.
Circle Theorem 1 - Tangents and Radii
The angle between a tangent and a radius is 90°, but they must come from the same arc. This is a key rule to keep in mind when working with circles and tangents.
Alternate Segment Theorem
The alternate segment theorem states that angles at the circumference are equal. This is an essential rule to remember when dealing with alternate segments in a circle.
When looking at the diagram, we are given the measure of a tangent as 76.6° with a value of 4.2. We need to find the value of OWD and WOQ given the common tangents to the circles with centers O and W.
In another scenario, we are given two circles with centers P and S. JKLM is a common tangent to the circles, while PQRS is a straight line. We need to solve for the value of x + y in this case.
Moving on to the third scenario, we have a common tangent AB to the circles centered in C and D. We need to find the value of x + y + z in this situation.
Finally, in the last scenario, we are given two circles centered P and Q with a common tangent ABCD. We are asked to find the value of x + y + z.
It's important to remember the rules and theorems of circle geometry when working through problems involving circles and quadrilaterals. Keeping these properties and theorems in mind will help to accurately solve circle geometry problems.
