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Learn about inscribed angles, their properties, theorems, and corollaries in circles. Discover how angles relate to intercepted arcs and chords in geometry.
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Section 9-5 Inscribed Angles
B C A D Inscribed angles • An angle whose vertex is on a circle and whose sides contain chords of the circle. are inscribed angles.
Theorem 9-7 • The measure of an inscribed angle is equal to half the measure of its intercepted arc.
If m = 45, then = R If then m = T A Example: 54
Corollary 1 • If two inscribed angles intercept the same arc, then the angles are congruent. 2 1
S Corollary 2 • An angle inscribed in a semicircle is a right angle. Circle S
Q U D A Corollary 3 • If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. are supplementary are supplementary
Theorem 9-8 • The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.
A is tangent to Circle O is a chord in Circle O O T P If m = 140, then = Example: