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Geometry Level 5

Let $\Delta PQR$ be the pedal triangle of $\Delta ABC$ . Excenters 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 $\Delta ABC$ .

Details and Assumptions:

Pedal triangle of a triangle is formed by joining feet of altitudes to the sides of the triangle.
An excenter of a triangle is a point of intersection of an internal angle bisector and two external angle bisectors of the triangle.

Note: Try to solve this within a minute.