Denote the feet of the altitudes by and respectively. Then
which can be summarized as follows:
Let be the pedal triangle of . Excenters of are .
If one of the vertices of is then find the area of .
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.