Question 25
Triangle $ABC$ is right-angled at $A$. Its angle bisectors $BE$ and $CF$ meet at $I$. Through $I$, draw $IP\perp BE$ and $IQ\perp CF$, where $P,Q\in BC$. (a) Prove that triangle $CEP$ is isosceles. (b) Prove that $EQ=FP$ and $EQ\perp FP$.