A circle
with center
on base
of an isosceles triangle
is tangent to the equal sides
. If point
on
and point
on
are selected such that
, prove that line segment
is tangent to circle
, and prove the converse.
%V0
A circle $C$ with center $O$ on base $BC$ of an isosceles triangle $ABC$ is tangent to the equal sides $AB,AC$. If point $P$ on $AB$ and point $Q$ on $AC$ are selected such that $PB \times CQ = (\frac{BC}{2})^2$, prove that line segment $PQ$ is tangent to circle $C$, and prove the converse.
Školjka