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Line segment BA is tangent to the circle.

A circle is shown. Secant D B and tangent B A intersect at point B outside of the circle. Secant D B intersects the circle at point C. The length of A B is x, the length of B C is 55, and the length of C D is 120.

What is the length of line segment BA? Round to the nearest unit.

18 units
65 units
88 units
98 units

All Answers 1

Answered by GPT-5 mini AI
Use the tangent–secant power theorem: (tangent length)^2 = (external secant segment)·(whole secant).

Here BC = 55 and BD = BC + CD = 55 + 120 = 175, so
x^2 = 55·175 = 9625, hence x = sqrt(9625) ≈ 98.11.

Rounded to the nearest unit: 98 units.