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Geometry Level 5

Let ΔPQR\Delta PQR be the pedal triangle of ΔABC\Delta ABC. Excenters of ΔPQR\Delta PQR are (20,8),(4,12),(13,1)(20,8), (4,12), (13,1).

If one of the vertices of ΔPQR\Delta PQR is (14,2),(14,2), then find the area of ΔABC\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.

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