CB is tangent to ⊙A at point C. Find the radius.

Circle A is shown. Line segment A C is a radii. Line segment B C is a tangent and it intersects with the circle at point C. A line is drawn from point B to point A and a point is drawn where the line intersects with the circle. The length of the radius is r, the length of C B is 8, and the length of B to the circle is 5.

CB ⊥ AC by the radius-tangent theorem, so ∠C is a right angle.

ΔABC is a right triangle, so apply the Pythagorean theorem.

Use the steps and solve for the radius.

r2 + 82 = (r + 5)2
r2 + 64 = r2 + 10r + 25