EXAMPLE 1 Find angle and arc measures

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Presentation transcript:

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

GUIDED PRACTICE for Example 1 Find the indicated measure. SOLUTION m RST = 2 (98o) = 196o

Find an angle measure inside a circle EXAMPLE 2 Find an angle measure inside a circle Find the value of x. SOLUTION The chords JL and KM intersect inside the circle. xo = 12 (mJM + mLK) Use Theorem 10.12. xo = 12 (130o + 156o) Substitute. xo = 143 Simplify.

Find an angle measure outside a circle EXAMPLE 3 Find an angle measure outside a circle Find the value of x. SOLUTION The tangent CD and the secant CB intersect outside the circle. m BCD (mAD – mBD) = 12 Use Theorem 10.13. = 12 (178o – 76o) xo Substitute. = 51 x Simplify.

GUIDED PRACTICE for Examples 2, 3, and 4 4. Find the value of the variable. y = 61o ANSWER

GUIDED PRACTICE for Examples 2, 3, and 4 5. Find the value of the variable. = 104o a ANSWER

Daily Homework Quiz Line t is tangent to the circle. Find the value of x and y. 4. ANSWER x = 81; y = 40.5