Answer:
x = 8
Explanation:
the angle between the tangent and the radius at the point of contact A is 90°
then Δ ABP is right at A
using Pythagoras' identity in the right triangle
BP² = AP² + AB² , that is
(x + 9)² = x² + 15² ← expand parenthesis on left side using FOIL
x² + 18x + 81 = x² + 225 ( subtract x² from both sides )
18x + 81 = 225 ( subtract 81 from both sides )
18x = 144 ( divide both sides by 18 )
x = 8