Question

Given the circle below with secant VUT and tangent ST, find the length of ST. Round to the nearest tenth if necessary.

Answer 1

ST ≈ 33.9

Explanation:

given a tangent and a secant drawn from an external point to the circle, then

the square of the measure of the tangent is equal to the product of the secant's external part and the entire secant , that is

ST² = TU × TV = 24 × (24 + 24) = 24 × 48 = 1152 ( take square root of both sides )

ST =
`√(1152)` ≈ 33.9 ( to the nearest tenth )