# 100 followers question

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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