Question

Use the circle to solve for the missing measures. Assume lines that appear tangent are tangent. Do NOT round any answers.

Answer 1

The given circle having two external tangents, according to circle

theorem, have the following values;

• r = 3

• m∠1  = 82°

• m∠2 = 49°

• x = 82°

How can the radial  length and angles be found?

r² + 1.6² = (0.4 + r)²

(0.4 + r)² - (r² + 1.6²) = 0

0.8·r - 2.4 = 0

0.8·r = 2.4

r = 2.4 ÷ 0.8 = 3

• r = 3

y = 49°

From the two tangent angle theorem, we have;

m∠1 = ((82 + 98 + 82) - (360 - ((82 + 98 + 82)))) ÷ 2 = 82

• m∠1  = 82°

According to circle theorems, angle at the center is twice angle

subtended at the circumference.

m∠2 = (360 - (82 + 98 + 82)) ÷ 2 = 49°

• m∠2 = 49°

The length of the chord subtended by the arc x is equal to the length of

the chord subtended by 89°, which gives;

• x = 82°

Learn more about circle theorems applications here:

brainly.com/question/16879446