Question 183
Let $ABC$ be an acute triangle with $AB \lt AC$, let $O$ be its circumcentre and let $A'$ be the reflection of $A$ in $BC$. The parallel through $O$ to $BC$ crosses $AC$ at $F$, and the tangent at $F$ to circle $BFC$ crosses the parallel through $A'$ to $BC$ at $M$. Consider the point $K$ on the ray $AB$, emanating from $A$, such that $AK = 4AB$. Prove that the orthocentre of the triangle $ABC$ lies on the circle on diameter $KM$.
Radu Lecoiu
Radu Lecoiu