$\vartriangle ABC$ is a triangle, $M$ the midpoint of $BC, D$ the projection of $M$ on $AC$ and $E$ the midppoint of $MD$. Prove that the lines $AE,BD$ are orthogonal if and only if $AB = AC$.
Source: 2013 Saudi Arabia Pre-TST 4.4
Tags: geometry, perpendicular, isosceles
$\vartriangle ABC$ is a triangle, $M$ the midpoint of $BC, D$ the projection of $M$ on $AC$ and $E$ the midppoint of $MD$. Prove that the lines $AE,BD$ are orthogonal if and only if $AB = AC$.