alicegrant88
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AC is tangent to circle O at A. The diagram is not drawn to scale.

If mBY =34 degrees, what is < YAC?

a. 68 degrees
b. 51 degrees
c. 73 degrees
d. 56 degrees

AC is tangent to circle O at A The diagram is not drawn to scale If mBY 34 degrees what is lt YAC a 68 degrees b 51 degrees c 73 degrees d 56 degrees class=

Respuesta :

nobillionaireNobley
Recall that a tangent to a circle is perpendicular to the diameter of the circle at the pont of tangency.

Given that AC is tangent to circle O at A, this means that line AB is a diameter of the circle.

Thus, angle BAC is a right angle.

Also, angle BAC = angle BAY + angle YAC.
i.e. 34 + <YAC = 90
<YAC = 90 - 34 = 56 degrees.
Lanuel

Since angle BAC is complimentary and a right angle, angle YAC is equal to: D. 56 degrees.

How to calculate the required angle?

At the pont of tangency, the tangent of a circle would be perpendicular to the diameter of the same circle. Since AC is a tangent to circle O at point A, it simply means that line AB is the diameter of circle O.

Therefore, we can deduce that angle BAC is complimentary and a right angle. Mathematically, this is given by:

<BAC = <BAY + <YAC.

90 = 34 + <YAC

<YAC = 90 - 34

<YAC = 56 degrees.

Read more on tangent here: https://brainly.com/question/16507124

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