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9-6 Secants, Tangents and Angle Measures

9-6 Secants, Tangents and Angle Measures. Secant A line that intersects a circle in exactly two points. Theorem 9-11 If a secant and a tangent intersect at the point of tangency, then the measure of the intercepted arc is twice the measure of the angle formed. Th. 9-11 m BC = 2( m ABC ).

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9-6 Secants, Tangents and Angle Measures

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  1. 9-6Secants, Tangents and Angle Measures

  2. SecantA line that intersects a circle in exactly two points.

  3. Theorem 9-11If a secant and a tangent intersect at the point of tangency, then the measure of the intercepted arc is twice the measure of the angle formed.

  4. Th. 9-11m BC =2(m ABC) A B C

  5. Theorem 9-12If two secants intersect in the interior of a circle, then the sum of the measures of the arcs intercepted by the angle and its vertical angle is twice the measure of the angle formed.

  6. Th. 9-12m PB + m RL = 2(m 1) R P 1 B L

  7. Theorem 9-13If two secants or tangents intersect outside a circle, then the difference of the measures of the intercepted arcs is twice the measure of the angle formed.

  8. Th. 9-13m AB – m RS = 2(m RMS) A R M S B

  9. B O 1 3 Y K 2 4 D A In circle K, mOB = 98, mOY = 28, mYD = 62, and mDA = 38. Find each measure. m<1 = 24 mAB = 90 m<3 = 132 m<2 = 36

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