Two distinct points $A$ and $B$ are on a circle with center at $O$, and point $P$ is outside the circle such that $\overline{PA}$ and $\overline{PB}$ are tangent to the circle. Find $AB$ if $PA = 12$ and the radius of the circle is 9.

AdminMod2
Sep 3, 2017

#1**+1 **

OA is a radius = 9

Because OAP is a right angle, OP = sqrt ( PA^2 + OA^2) = sqrt (12^2 + 9^2) =

sqrt (225) = 15

Let AB intersect OP at R

And triangles OPA and OAR are similar

So

PA / OP = AR / OA

12 / 15 = AR / 9

AR = 108/15 = 36/5

And AR = (1/2) AB ...so

AB = 2 (AR) = 2(36/5) = 72/5

CPhill
Sep 3, 2017

#2**0 **

Two distinct points $A$ and $B$ are on a circle with center at $O$, and point $P$ is outside the circle such that $\overline{PA}$ and $\overline{PB}$ are tangent to the circle. Find $AB$ if $PA = 12$ and the radius of the circle is 9.

see: https://web2.0calc.com/questions/circle-tangent

heureka
Sep 4, 2017