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 $\Delta ABC$ .

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Details and Assumptions:
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- 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.

The answer is 70.

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Excentres of pedal triangle of a triangle are nothing but the vertices of triangle itself. Hence area of $\Delta ABC = \dfrac { 1 }{ 2 } \times \begin{vmatrix} 20 & 8 & 1 \\ 4 & 12 & 1 \\ 13 & 1 & 1 \end{vmatrix} = 70 sq. units$