An inscribed angle is an angle whose vertex is on a circle and whose sides (arms) are chords of the circle. The intercepted arc is the part of the circle contained within the arms of the angle. According to the theorem, an inscribed angle is equal to half of its intercepted arc. Two corollaries are that an angle inscribed in a semicircle is a right angle, and the opposite angles of a quadrilateral inscribed in a circle are supplementary.

1. 9-5 Inscribed Angles

2. Inscribed angle – An angle where the vertex is on the circle and its arms are chords in the circle. Inscribed angle

3. Intercepted arc – the part of the circle inside the arms of the angle Intercepted arc

4. Lets go to the internet… Circle Fun

5. Theorem – An inscribed angle is half of the intercepted arc.

6. What is the measure of x? 50° 60 40° 20° 10° 10 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

7. What is the measure of y? 50° 60° 40° 20° 10° 10 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

8. Corollary 1 – If two inscribed angles intercept the same arc, then the angles are congruent. 1 2

9. Lets go to the internet… Circle Fun

10. Corollary 2 – An angle inscribed in a semicircle is a right angle.

11. Corollary 3 – If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. F E D G m  D + m  F = 180 ° m  E + m  G = 180 °

12. What is x? 30° 40° 70° 90° 110° 140° 150° 10 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

13. What is y? 30° 40° 70° 90° 110° 140° 150° 10 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

14. What is z? 30° 40° 70° 90° 110° 140° 150° 10 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

15. Lets go to the internet… Circle Fun

16. Theorem – The measure of an  formed by a chord and a tangent is equal to ½ the intercepted arc. 1

17. SPICSA Page 354 2-10 even