Let
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
be the circumcenter and
![H](/media/m/4/c/0/4c0872a89da410a25f00b86366efece7.png)
the orthocenter of an acute-angled triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
such that
![BC>CA](/media/m/e/e/6/ee6181c3af241e3b83282447f7d648de.png)
. Let
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
be the foot of the altitude
![CH](/media/m/2/3/e/23ed2333fb496208650ffe4025f71601.png)
of triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
. The perpendicular to the line
![OF](/media/m/8/b/4/8b4754414783aed303bb8fafc724ff22.png)
at the point
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
intersects the line
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
at
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
. Prove that
![\measuredangle FHP=\measuredangle BAC](/media/m/8/0/5/805ed2f530f2745fde7a51339762d5da.png)
.
%V0
Let $O$ be the circumcenter and $H$ the orthocenter of an acute-angled triangle $ABC$ such that $BC>CA$. Let $F$ be the foot of the altitude $CH$ of triangle $ABC$. The perpendicular to the line $OF$ at the point $F$ intersects the line $AC$ at $P$. Prove that $\measuredangle FHP=\measuredangle BAC$.