Question

A circle is shown. A secant goes through the center point and intersects a tangent at a point outside of the circle. The length of the tangent is 7 inches. The length of the external part of the secant is 4 inches.
Kylie writes an equation to solve for the diameter, d, of the circle shown. Solve Kylie’s equation to find the diameter of the circle.

4 (d + 4) = 72

What is the diameter?

7.5 in.
8.25 in.
11.25 in.
13.25 in.

Answer 1

Use the tangent-secant theorem: (tangent)^2 = (external secant) × (entire secant). So
7^2 = 4(d + 4) → 49 = 4(d + 4) → d + 4 = 49/4 = 12.25 → d = 12.25 − 4 = 8.25 in.

(The given 72 is a mistake; the correct diameter is 8.25 in.)