Question

Use the image to answer the question.

A circle has center point upper O. Upper O connects to a point on the circumference labeled upper B. Upper B connects to a point outside the circle labeled upper A. A diagonal line connects upper A and upper O to form the shape of a triangle.

If BO=45
in. and BA=108
in., then what is the length of AO
to the nearest whole inch?

(1 point)
Responses

117 in.
117 in.

25 in.
25 in.

67 in.
67 in.

98 in.

Answer 1

If AB is tangent at B, then OB ⟂ AB, so triangle AOB is right with legs OB = 45 and AB = 108. By the Pythagorean theorem:

AO = sqrt(45^2 + 108^2) = sqrt(2025 + 11664) = sqrt(13689) = 117 in.

Answer: 117 in.