1. Sect. 12-4 Inscribed Angles Geometry Honors

2. What and Why What? – Find the measure of inscribed angles and the arcs they intercept. Why? – To use the relationships between inscribed angles and arcs in real-world situations, such as motion pictures.

3. Recall Central Angle A central angle is an angle whose vertex is the center of the circle. The arc formed by a central angle is the same measure as the angle.

4. Inscribed Angles

5. Measuring Inscribed Angles

6. Example

7. Theorem 12-10 Inscribed Angle Theorem

8. There are three cases of this theorem to consider. Case 1: The center is on a side of the angle.

9. Case 2 The center is inside the angle.

10. Case 3 The center is outside the angle.

11. Example Find the values of a and b in the diagram.

12. Corollaries Corollary 1 – Two inscribed angles that intercept the same arc are congruent. Corollary 2 – An angle inscribed in a semicircle is a right angle. Corollary 3 – The opposite angles of a quadrilateral inscribed in a circle are supplementary.

13. Examples Find the measure of the numbered angle.

15. Theorem 12-11 The measure of an angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.

16. Example