Question

Find the length and diameter of the circle if ab is tangent to p

Answer 1

diameter = 16

Explanation:

given AB is a tangent to the circle then ∠ PBA = 90° and Δ ABP is right

using Pythagoras' identity in the right triangle

BP² + AB² = AP²

BP² + 15² = 17²

BP² + 225 = 289 ( subtract 225 from both sides )

BP² = 64 ( take square root of both sides )

BP =
`√(64)` = 8

now BP is the radius of the circle , so

diameter = 2 × BP = 2 × 8 = 16