Question

In the figure below, the segment that appears to be tangent to the circle is tangent to the circle. Which of the following is the length of the diameter of the circle to the nearest tenth of a unit?

A. 41.7

B. 26.7

C.16.0

D. 9.0

Answer 1

Explanation:

Check attachment for diagram,

Since line AB is tangent to the circle then, <OAB is a right angle,

Then, we can apply Pythagoras theorem to the right angle triangle,

NOTE: from the centre of the circle to the tangent point at A is the radius of the circle,

And also, the total length of OB is

OB = r + 15

Then, applying Pythagorean theorem

OB² = OA² + AB²

(r+15)² = r² + 25²

(r+15)(r+15) = r² + 625

r² + 15r + 15r + 225 = r² + 625

Collect like terms

r² + 30r - r² = 625 - 225

30r = 400

Divide both sides by 30

r = 400 / 30

r = 13.33

So, the diameter of the circle is related to the radius by the relation

Diameter = 2 × radius

d = 2 × r

d = 2 × 13.33

d = 26.67

To the nearest tenth implies that to 1d•p

d ≈ 26.7

So, the diameter of the circle is 26.7