Question

If AD = 26 and AB = 24, calculate length of line segment BD. Segment AC is tangent to circle D.

Answer 1

BD = 10

Explanation:

Since AC is a tangent to the circle at B then ∠ABD = 90°

Using Pythagoras' identity in the right triangle ABD with hypotenuse AD

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

BD² + AB² = AD²

BD² + 24² = 26²

BD² + 576 = 676 ( subtract 576 from both sides )

BD² = 100 ( take the square root of both sides )

BD =
`√(100)` = 10