# 100 followers question

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 foots 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.

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