Question

10 In the

accompanying diagram, PA is tangent to
circle O at A and PBC is a secant. If CB = 9 and
PB = 3, find the length of PA.
C
0°
8
A
a
CB=9
PB = 3
PA=X
5

Answer 1

PA = 6

Explanation:

given a tangent and a secant drawn from an external point to the circle , then the square of the tangent is equal to the product of the secant's external part and the entire secant , that is

PA² = PB × PC = 3 × (3 + 9) = 3 × 12 = 36 ( take square root of both sides )

PA =
`√(36)` = 6