Hexagon Area

Geometry Level 4

Triangle ABCABC has area [ABC]=468 [ABC] = 468 . D,ED, E and FF are the midpoints of BC,CABC, CA and ABAB, respectively. Points P,QP, Q and RR are defined such that PP is the incenter of AEFAEF, QQ is the incenter of BFDBFD, and RR is the incenter of CDECDE. What is [DREPFQ] [DREPFQ] ?

Details and assumptions

[PQRS][PQRS] denotes the area of figure PQRSPQRS.

The incenter of a triangle is the center of the circle which is inscribed in the triangle such that it is tangent to all 3 sides.

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