Question 25
In a triangle $ABC$, the incircle $\omega$ centred at $I$ touches the sides $BC,CA$ and $AB$ at $D,E$ and $F$ respectively. $Q$ is the point on $\omega$ diametrically opposite to $D$, and $P$ is the intersection of the lines $FQ$ and $DE$. Suppose that $BC=50$ cm, $CA=49$ cm and $PQ=QF$. Determine the length of $AB$ in centimetres.