# Euler's Theorem for Pedal Triangles

Euler's Theorem for Pedal Triangles

Let ABC be a triangle and P an arbitrary point. Let A', B', and C' be the feet of the perpendiculars from P to the sides of ABC. Let O and R be the center and radius of the circumcircle. Then .

area(A'B'C')=1-area(ABC)

1

4

2

OP

2

R