Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its measure.

 An inscribed angle is an angle whose vertex is on a circle. Inscribed Angle

 The arc that lies in the interior of an inscribed angle and has endpoints on the angle. Intercepted Arc

 The measure of an inscribed angle is half the measure of its intercepted arc. Measure of an Inscribed Angle Theorem

Theorem 10.8  If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

Inscribed Polygon  A polygon is an inscribed polygon if all of its vertices lie on a circle.  The circle that contains the vertices is circumscribed circle.

 If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle. Theorem 10.9

 A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. Theorem 10.10

Inscribed vs. Central Angles  If the measure of an inscribed angle is 60 o, what is the measure of its intercepted arc?  If the measure of a central angle is 60 o, what is the measure of its intercepted arc?

 P. 676 #1-25 all Assignment