Question 100
Let $\triangle ABC$ be an acute-angled triangle, with $\angle B \neq \angle C$. Let $M$ be the midpoint of side $BC$, and $E$, $F$ be the feet of the altitudes from $B$, $C$, respectively. Denote by $K$, $L$ the midpoints of segments $ME$, $MF$, respectively. Suppose $T$ is a point on the line $KL$ such that $AT \parallel BC$.
Prove that $TA = TM$.
Prove that $TA = TM$.