1. Inscribed Angles 10.3 California State Standards
4: Prove theorems involving congruent and similar
7: Prove/use theorems involving circles.
16: Find probability given graph or table
21: Prove/solve relationships with circles.

2. definition Inscribed Angle An angle whose vertex is on a circle and
whose sides contain chords of the circle. P
inscribed angle Q R

3. definition Intercepted Arc
An arc that lies in the interior of an inscribed angle
and has endpoints on the angle. P
intercepted arc Q R

4. definitions Inscribed Polygon Circumscribe
A polygon with all of its vertices on a circle.
Circumscribe
To circle around something. B C A D P F E

5. theorem Inscribed Angle Measure A B C
The measure of an inscribed angle
is half the measure of its intercepted arc. A B C

6. example
Find the measure of the arc or angle. B
140o
70o A C D

7. theorem Congruent Inscribed Angles Inscribed angles are congruent.
that intercept the same arc B E A C

8. example 45o 45o 45o Find the measure of the arc or angle. C B A D E

9. theorem Inscribed Right Triangle An inscribed right triangle
has a diameter as its hypotenuse. P C Q R

10. example
Find the measure of the arc or angle. B
180o C D A

11. theorem Inscribed Quadrilateral
A quadrilateral can be inscribed in a circle
if and only if its opposite angles are supplementary. P S Q R

12. example
Find value of x. S T xo yo
85o
80o R U

13. example
Find the measure of the arc or angle. B
98o C A
196o D

14. example
Find the measure of the arc or angle. C B
44o
44o A D

15. example
Find value of x. B C
3xo A

16. example Find value of the measure of each angle. B A C D 19yo 10yo
40xo
22xo D

17. example Find value of the measure of each angle. B A C D 114o 19yo
40xo
22xo
66o D