Question 132
Let $T$ be the centroid of triangle $ABC$ and $D$ the midpoint of side $BC$. Let the lines $AT$, $BT$ and $CT$ meet the circumcircle of triangle $ABC$ again at the points $P$, $Q$ and $R$, respectively. Suppose that $|AD|=\frac{\sqrt{3}}{2}|AC|$. Prove that triangle $PQR$ is isosceles.