tangent circles

Question

line segements PA and Pb are tangeng segments from point P

1.)if OA=6cm and PA=8cm find OP.

2.)If OP=13cm and PA=12cm find OA.

Answer 1

Because PA is a tangent to circle centre O, the angle A is 90°, so OAP is a right triangle with OP as the hypotenuse. By Pythagoras, OP²=OA²+PA², so

(1) OP²=36+64=100, and OP=10

(2) OA²=169-144=25, and OA=5