Question 2
Let $ABC$ be an acute-angled triangle, and let $D,E,F$ be the midpoints of $BC,CA,AB$, respectively. Construct a circle centred at the orthocentre of triangle $ABC$ such that triangle $ABC$ lies in the interior of the circle. Extend $EF$ to meet the circle at $P$, $FD$ to meet it at $Q$, and $DE$ to meet it at $R$. Show that $AP=BQ=CR$.