1. Notes 12.3/12.4 (Angles) Learning Targets:
I can find the measure of an inscribed angle.
I can find the measure of an angle formed by a tangent and a chord.
I can find measures of angles formed by chords, secants and tangents.

2. Vocabulary
Tangent – a line, ray or segment that intersects the circle at one point
Chord - a segment whose endpoints are on the circle
Secant – a line, ray or segment that intersects the circle at two points

3. Inscribed Angle
Inscribed Angle: An angle whose vertex lies on a circle and whose sides are chords of the circle (or one side tangent to the circle).
Examples: 3 1 2 4
No!
Yes!
No!
Yes!

4. Inscribed Angle Theorem
The measure of an inscribed angle is equal to ½ the measure of the intercepted arc. Y
Inscribed Angle
110
55 Z
Intercepted Arc

13. Example: Interior Angle Theorem
91 A C x° y° B D
85

14. Exterior Angles
An angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle. 3 y x 2 1
Two secants
2 tangents
A secant and a tangent

15. Exterior Angle Theorem
The measure of the angle formed is equal to ½ the difference of the intercepted arcs.

16. Example: Exterior Angle Theorem