1. Section 10.3 Inscribed Angles

2. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

3. Intercepted Arc An arc formed from an inscribed angle on a circle. Intercepted Arc

4. Measure of an Inscribed Angle Half the measure of its intercepted arc m  ADB = ½ m AB OR m AB = 2(m  ADB) 50° 100°

5. Examples #1-6

6. Theorem 10.9 If two inscribed angles of a circle intercept the same arc, then the angles are congruent. A C B D  C is congruent to  D It is given that m  E  75 . What is the m  F? 75  G E F H m  F = 75 

7. Inscribed All of the vertices of a polygon lie on a circle

8. Circumsribed Surrounding the figure

9. Theorem 10.10 If a right triangle is inscribed in a circle, then the hypotenuse is the diameter.  B is a right angle iff AC is the diameter A B C

10. Theorem 10.11 A quadrilateral can be inscribed in a circle iff its opposite angles are supplementary (180°) m  D + m  F  180  m  E + m  G  180 

11. Examples #1-6