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10-5 Apply Other Angle Relationships in Circles

10-5 Apply Other Angle Relationships in Circles. Chord/Tangent Theorem. C. If a chord and a tangent intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. B. 2. 1. A. m 1 = ½ m AB m 2 = ½ m BCA.

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10-5 Apply Other Angle Relationships in Circles

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  1. 10-5 Apply Other Angle Relationships in Circles

  2. Chord/Tangent Theorem C If a chord and a tangent intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. B 2 1 A m 1 = ½mAB m 2 = ½ mBCA

  3. Findm 1 and m 2. Find the other arc: 360° – 120° = 240° B ° 120° ° 2 1 A

  4. Chord/Chord Theorem The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs n p m + n = p 2 m

  5. example: solve for x 80º 2 • • 2 50º xº

  6. Angles Outside the Circle Theorem The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs.

  7. Secant/Tangent Theorem If a secant segment and a tangent segment share an endpoint outside of a circle, then B A C D

  8. example: find x. B A x ̊ 55 ̊ 125 ̊ 125 – 55 = x 2 70 = x 2 35 = x D

  9. Secant/Secant Theorem If a secant segment and a tangent segment share an endpoint outside of a circle, then C D B E A

  10. example: solve for x 100 – x = 40 2 __ 1 40 ̊ 100 – x = 80 -x = -20 x ̊ x = 20° 100 ̊

  11. Tangent/Tangent Theorem If a Tangent segment and a tangent segment share an endpoint outside of a circle, then B A C D

  12. example: solve for x 220 ̊ 1st : Find the other arc 360 – 140 = 220 220 – 140 = x 2 140 ̊ 80 = x 2 x ̊ 40 ̊ = x

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