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Ac is tangent to circle O at A. The diagram is not drawn to scale. If m by=52 degrees what is m yac?

A. 38°
B.64°
C.78°
D.104°

Ac is tangent to circle O at A The diagram is not drawn to scale If m by52 degrees what is m yac A 38 B64 C78 D104 class=

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kudzordzifrancis

ANSWER

A. 38°

EXPLANATION

The tangent, AC to the circle meets the diameter AB to the circle at right angle.

This implies that,

[tex]m \angle BAY + m \angle YAC = 90 \degree[/tex]

Substitute the given angle:

[tex]52 \degree + m \angle YAC = 90 \degree[/tex]

[tex]m \angle YAC = 90 \degree - 52 \degree[/tex]

[tex]m \angle YAC = 38 \degree[/tex]

akposevictor

Using the tangent theorem and the inscribed angle theorem, m∠YAC is: A. 38°

What is the Tangent Theorem?

According to the tangent theorem, a right angle (90°) is formed at the point of intersection between the radius and the tangent of a circle.

m∠BAY = m(BY) = 52° (inscribed angle theorem)

m∠BAC = 90° (tangent theorem)

m∠YAC = m∠BAC - m∠BAY

Substitute

m∠YAC = 90 - 52 = 38°

Learn more about the tangent theorem on:

https://brainly.com/question/9892082

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