Page 1: Understanding Inscribed Angles and Circle Theorems

This page introduces fundamental concepts about inscribed angles that intercept the diameter of the circle and related theorems. The content begins with essential definitions and progresses through key theorems and practical examples.

Definition: An inscribed angle is an angle whose vertex lies on a circle and whose sides are chords of the circle.

Highlight: The inscribed angle of a circle formula states that the measure of an inscribed angle is half the measure of its intercepted arc.

The page presents three important corollaries:

Vocabulary: Corollary One states that two inscribed angles intercepting the same arc are congruent. Vocabulary: Corollary Two establishes that an angle inscribed in a semicircle is a right angle. Vocabulary: Corollary Three declares that opposite angles of an inscribed quadrilateral are supplementary.

The tangent chord theorem is also introduced:

Definition: The measure of an angle formed by a tangent and a chord equals half the measure of the intercepted arc.

Two detailed examples are provided to demonstrate practical applications:

Example: Example One involves finding values of angles 'a' and 'b' using the inscribed angle theorem, where one angle measures 60° and creates an arc of 120°.

Example: Example Two shows how to find an angle formed by a tangent and chord, where mPMQ = 212° and the solution requires applying the tangent-chord theorem to find mLPQR = 74°.

The page concludes with an essential understanding statement:

Highlight: Angles formed by intersecting lines have special relationships to the arcs they intercept, forming the foundation for understanding circle geometry.