In the figure, $AP$ is tangent to the circle centered at $O$, $AB=BC,$ and $AP=3\sqrt{2}$. Find the length of $AC$.
3sqrt (2) = sqrt (18)
Using the secant tangent theorem
AP^2 = AB ( AB + BC)
Since AB =BC then let them = x
AP^2 = x ( x + x)
(sqrt 18)^2 = x (2x)
18 = 2x^2 divide both sides by 2
9 = x^2
3 = x
So
AC = 2x = 2 (3) = 6
