Question

In the following figure, a tangent segment $PA$ touching a circle in $A$ and a secant $PBC$ intersects the circle at points $C$ and $B$. If $AP=13$ and $BP=6$, find $PC$

Answer 1

In the given figure,
$PA$ is the tangent segment touching circle at point $A$ and $PC$ is the second intersecting circle at points $B$ and $C$.
$AP=13,BP=6$ ....(Given)
and $PC=?$
By the tangent secant property,
$A{P}^2=PB\times PC$
$\Rightarrow (13{)}^2=6\times PC$
$\Rightarrow 169=6\times PC$
$\Rightarrow PC=\frac{169}{6}=28.17$ units