Question 90
Let $ABC$ be an acute triangle with circumcircle $w$ with center $O$. Let $A_0$ and $C_0$ be the second intersection points of $w$ with the continuation of the altitudes from $A$ and $C$. Let $A_1$ and $C_1$ be the intersection points of the line $A_0C_0$ with the sides of the triangle $AB$ and $BC$ respectively. Let $A_2$ and $C_2$ be the points of $AC$ such that $A_2O \parallel BC$, and $C_2O \parallel AB$. Let $H$ – orthocenter of $\triangle ABC$, $T$ is the intersection point $A_1A_2$ and $C_1C_2$. Prove that $HT \parallel AC$.
(Anton Trygub)
(Anton Trygub)