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Geometry Level 4

Let \(\Delta PQR\) be the pedal triangle of \(\Delta ABC\). Excentres of \(\Delta PQR\) are \((20,8),~(4,12)~\& ~ (13,1)\). If one of the vertices of \(\Delta PQR\) is \((14,2)\) then find the area of \(\Delta ABC\).

Bonus: Try to solve this within a minute.

Details and Assumptions

Pedal Triangle of a triangle is formed by joining foot of altitudes to a side of the triangle.
Excentres of a triangle are point of intersection of an internal angle bisector and two external angle bisectors of the triangle.

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