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Section 9-5

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,

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Section 9-5

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  1. Section 9-5 Inscribed Angles

  2. 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.

  3. Theorem 9-7 • The measure of an inscribed angle is equal to half the measure of its intercepted arc.

  4. If m = 45, then = R If then m = T A Example: 54

  5. Corollary 1 • If two inscribed angles intercept the same arc, then the angles are congruent. 2 1

  6. S Corollary 2 • An angle inscribed in a semicircle is a right angle. Circle S

  7. Q U D A Corollary 3 • If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. are supplementary are supplementary

  8. 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.

  9. A is tangent to Circle O is a chord in Circle O O T P If m = 140, then = Example:

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