In the plane let
![\,C\,](/media/m/b/a/a/baadd742c8e5e51598730598d31424c8.png)
be a circle,
![\,L\,](/media/m/e/5/0/e5043ef29a8f3709faafcf1f117f66c9.png)
a line tangent to the circle
![\,C,\,](/media/m/c/4/d/c4dc1a86fcc9cface2541706275b28e2.png)
and
![\,M\,](/media/m/c/9/f/c9f91b46086825956d8014489d29f699.png)
a point on
![\,L](/media/m/c/0/0/c00bf320e5ed68e5e56df2772bbb4680.png)
. Find the locus of all points
![\,P\,](/media/m/7/9/7/79743447988dfd17a0bf256451541cf0.png)
with the following property: there exists two points
![\,Q,R\,](/media/m/e/d/6/ed6398fec122130284ae5379f0d53cc5.png)
on
![\,L\,](/media/m/e/5/0/e5043ef29a8f3709faafcf1f117f66c9.png)
such that
![\,M\,](/media/m/c/9/f/c9f91b46086825956d8014489d29f699.png)
is the midpoint of
![\,QR\,](/media/m/e/e/b/eeb9f93ce4a79fe3c7881202a90032c4.png)
and
![\,C\,](/media/m/b/a/a/baadd742c8e5e51598730598d31424c8.png)
is the inscribed circle of triangle
![\,PQR](/media/m/8/b/2/8b2d11751fafe1b8a68a4156947513c1.png)
.
%V0
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 $\,PQR$.