In the plane let
be a circle,
a line tangent to the circle
and
a point on
. Find the locus of all points
with the following property: there exists two points
on
such that
is the midpoint of
and
is the inscribed circle of triangle
.
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In the plane let $\,C\,$ be a circle, $\,L\,$ a line tangent to the circle $\,C,\,$ and $\,M\,$ a point on $\,L$. Find the locus of all points $\,P\,$ with the following property: there exists two points $\,Q,R\,$ on $\,L\,$ such that $\,M\,$ is the midpoint of $\,QR\,$ and $\,C\,$ is the inscribed circle of triangle $\,PQR$.
Školjka