Question 25
The incircle of the triangle $ABC$ centred at $I$ touches the sides $BC,CA,AB$ at $D,E,F$ respectively. Let $D'$ be the intersection of the extension of $ID$ with the circle through $B,I,C$; $E'$ be the intersection of the extension of $IE$ with the circle through $A,I,C$; and $F'$ the intersection of the extension of $IF$ with the circle through $A,I,B$. Suppose $AB=52$, $BC=56$, $CA=60$. Find $DD'+EE'+FF'$.