Question

AC is tangent to circle O at A. The Diagram is not to scale.

If mBY = 52 what is YAC?
I know the answer is B) 64, But Can someone show me the work?

Answer 1

m∠BAY = 1/2(52°) = 26°

m∠BAC = 90°

m∠YAC = m∠BAC - m∠BAY

m∠YAC = 90° - 26° = 64°

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Answer 2

• B. 64°

Explanation:

Given:

• mBY = 52°

Inscribed angle measure is half the intercepted arc:

• m∠BAY = 1/2(52°) = 26°

The angle between the diameter and tangent is right angle:

• m∠BAC = 90°

According to angle addition postulate:

• m∠YAC = m∠BAC - m∠BAY
• m∠YAC = 90° - 26° = 64°

Correct choice is B