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.

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

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

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

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

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

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

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

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

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

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

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

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

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

example Find value of x. B C 3xo A

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

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