Circles and inscribed angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle

Intercepted arc The arc formed by an inscribed angle is the intercepted arc of that angle. Arc AC is the intercepted arc of angle ABC

Theorem 47-1 The measure of an inscribed angle is equal to half the measure of its intercepted arc m< ABC = 1/2 m arc AC 50o 25o

Theorem 47-2 If an inscribed angle intercepts a semicircle, then it is a right angle

Proving and applying inscribed angle theorem 1) name inscribed angle 2) name arc intercepted by it 3) if m< COD = 52, find m <CBD D

Finding angle measures in inscribed triangles Find the measures of the 3 angles in the triangle 90o

Theorem 47-3 If 2 inscribed angles intercept the same arc, then they are congruent

Theorem 47-4 If a quadrilateral is inscribed in a circle, then it has supplementary opposite angles.

Finding angle measures in inscribed quadrilaterals <A = 4z , < C = 3z+5 Find <C