I have an acute angled triangle $ABC$ with $H$ as the orthocentre of the triangle. Let $DEF$ be the orthic triangle of triangle $ABC$. $D',E',F'$ are the reflections of H on sides $BC,CA,AB$. $A'$ is the point of intersection of circumcircle with diameter $HD'$. Define $B',C'$ similarly. Prove that $AA',BB',CC'$ are concurrent at a point on the euler line of triangle $ABC$.

How do I prove this?


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