Apply Other Angle Relationships in Circles

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Presentation transcript:

Apply Other Angle Relationships in Circles Warm Up Lesson Presentation Lesson Quiz

Warm-Up Solve for x. 1. 2x = 84 + 32 ANSWER 58 2. x = ( 360 – 120) = 0 1 2 ANSWER 120 3. 180 – x = ((2x + 4) + 28) 1 2 ANSWER 82

Warm-Up 4. One-half of the measure of an angle plus the angle’s supplement is equal to the measure of the angle. Find the measure of the angle. ANSWER 120

Example 1 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 Find the indicated measure. 1. m1 105° ANSWER

Guided Practice Find the indicated measure. 2. mRST 196° ANSWER

Guided Practice Find the indicated measure. 3. mXY 160° ANSWER

The chords JL and KM intersect inside the circle. Example 2 Find the value of x. SOLUTION The chords JL and KM intersect inside the circle. x° = 12 (mJM + mLK) Use Theorem 10.12. x° = 12 (130° + 156°) Substitute. x = 143 Simplify.

The tangent CD and the secant CB intersect outside the circle. Example 3 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 (178° – 76°) x° Substitute. = 51 x Simplify.

Example 4 The Northern Lights are bright flashes of colored light between 50 and 200 miles above Earth. Suppose a flash occurs 150 miles above Earth. What is the measure of arc BD, the portion of Earth from which the flash is visible? (Earth’s radius is approximately 4000 miles.) SCIENCE

Because CB and CD are tangents, CB AB and CD AD Example 4 SOLUTION Because CB and CD are tangents, CB AB and CD AD Also, BC DC and CA CA . So, ABC ADC by the Hypotenuse-Leg Congruence Theorem, and BCA DCA.Solve right CBA to find that m BCA 74.5°. = 12 m BCD (mDEB – mBD) Use Theorem 10.13. 149° 12 [(360° – x°) –x°] Substitute. x 31 Solve for x. The measure of the arc from which the flash is visible is about 31°.

Guided Practice Find the value of the variable. 4. y = 61 ANSWER

Guided Practice Find the value of the variable. 5. a = 104 ANSWER

Guided Practice Find the value of the variable. 6. x = about 253.7 ANSWER

Lesson Quiz Line t is tangent to the circle. Find the value of x and y. 1. ANSWER 115

Lesson Quiz Line t is tangent to the circle. Find the value of x and y. 2. ANSWER 52

Lesson Quiz Line t is tangent to the circle. Find the value of x and y. 3. ANSWER 25

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