Denote the feet of the altitudes by \(A', B',\) and \(C'\) respectively. Then,
\[\angle AA'B' = AA'C', \angle BB'C' = \angle BB'A', \angle CC'A' = \angle CC'B'\]
which can be summarized as
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.
This problem is created by me.