Section 10.3

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) 100° 50°

5. Examples #1-6

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

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. A B is a right angle iff AC is the diameter C B

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