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MM2G3b Understand and use properties of central, inscribed, and related angles

Standard. MM2G3b Understand and use properties of central, inscribed, and related angles. Theorem 6.13. If a tangent and a chord intersect at a point on the circle, then the measure of each angle formed is one half the measure of its intercepted arc. =. a. m 1. 12. (130 o ). (125 o ).

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MM2G3b Understand and use properties of central, inscribed, and related angles

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  1. Standard MM2G3b Understand and use properties of central, inscribed, and related angles

  2. Theorem 6.13 If a tangent and a chord intersect at a point on the circle, then the measure of each angle formed is one half the measure of its intercepted arc.

  3. = a. m1 12 (130o) (125o) 2 = b. m KJL EXAMPLE 1 Line mis tangent to the circle. Find the measure of the red angle or arc. SOLUTION = 65o = 250o

  4. = m1 12 (210o) GUIDED PRACTICE Find the indicated measure. SOLUTION = 105o

  5. m RST (98o) 2 = GUIDED PRACTICE Find the indicated measure. SOLUTION = 196o

  6. m XY (80o) 2 = GUIDED PRACTICE Find the indicated measure. SOLUTION = 160o

  7. Theorem 6.14 If two chords intersect INSIDE a circle, then the measure of each angle is one half the SUM of the measures of the arcs intercepted by the angle and its vertical angle.

  8. The chords JLand KMintersect inside the circle. (mJM + mLK) xo = 12 12 xo (130o + 156o) = xo = 143 EXAMPLE 2 Find the value of x. SOLUTION Use Theorem 10.12. Substitute. Simplify.

  9. Theorem 6.15 If a tangent and a secant, two tangents, or two secants intersect OUTSIDE a circle, then the measure of the angle formed is one half the DIFFERENCE of the measures of the intercepted arcs

  10. The tangent CDand the secant CBintersect outside the circle. (mAD – mBD) m BCD = 12 12 xo (178o – 76o) = x = 51 EXAMPLE 3 Find the value of x. SOLUTION Use Theorem 10.13. Substitute. Simplify.

  11. ANSWER y = 61o GUIDED PRACTICE 4. Find the value of the variable.

  12. ANSWER a = 104o GUIDED PRACTICE Find the value of the variable. 5.

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