Question

In the following figure, a tangent segment $PA$ touching a circle in $A$ and a secant $PBC$ are shown: If $AP=12,BP=9$, find $BC$.

Answer 1

We have, seg $PA$ is tangent and $PBC$ is a secant.
and $AP=12,BP=9$
$\therefore PB\times PC=P{A}^2$
$9\times PC=(12{)}^2$
$\therefore PC=\frac{144}{9}=16$
$\therefore BC=7$