# Other Angle Relationships in Circles Section 10.4

## Presentation on theme: "Other Angle Relationships in Circles Section 10.4"— Presentation transcript:

Other Angle Relationships in Circles Section 10.4
Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.

Theorem 10.12 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. C B A

Example C B A D

Lines Intersecting On, Inside, or Outside a Circle
On the circle Inside the circle Outside the circle Case Case Case 3 An inscribed angle

Lines, or chords, intersecting inside a circle Theorem 10.13
If two chords intersect in the interior of a circle, then the measures of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle. D A C B

Chords, intersecting inside a circle Example
B

Lines Intersecting Outside a Circle Three scenarios!
tangent-secant tangent-tangent secant-secant

Tangent - Secant Tangent-Secant A B C

Tangent - Tangent Tangent-Tangent P Q R

Secant - Secant Secant-Secant A D B C

Example Find x: A B C

Example Find x:

Example Find x:

Example Find x: