Point
lies on side
of a convex quadrilateral
. Let
be the incircle of triangle
, and let
be its incenter. Suppose that
is tangent to the incircles of triangles
and
at points
and
, respectively. Let lines
and
meet at
, and let lines
and
meet at
. Prove that points
,
, and
are collinear.
Author: Waldemar Pompe, Poland
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
![\omega](/media/m/d/5/8/d58b95547061c22be95770ed7010f287.png)
![CPD](/media/m/9/d/1/9d18a9d1ae10658cea5a459bf7f7ff88.png)
![I](/media/m/3/8/6/38689d6affa9ba35368ca4d3d76ea147.png)
![\omega](/media/m/d/5/8/d58b95547061c22be95770ed7010f287.png)
![APD](/media/m/5/f/0/5f0d8f53b46f1d7515af208c6cd58339.png)
![BPC](/media/m/4/4/0/440b9609d991a008cee182246acbb9d6.png)
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
![L](/media/m/f/c/1/fc1ae4eb78da7d1352cbf1f8217ab286.png)
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![AK](/media/m/a/8/d/a8daea05270451c22d9b8a7dd2502b68.png)
![BL](/media/m/d/6/0/d60f78c5ee392997e29360a340fd3fba.png)
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![I](/media/m/3/8/6/38689d6affa9ba35368ca4d3d76ea147.png)
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
Author: Waldemar Pompe, Poland