Sums of Squares of Segments Created by a Pedal Triangle

AC'	≈	5.15	BA'	≈	9.60	CB'	≈	6.69
C'B	≈	8.26	A'C	≈	5.65	B'A	≈	7.95

2

AC'

+

2

BA'

+

2

CB'

≈

163.38

2

C'B

+

2

A'C

+

2

B'A

≈

163.38

The triangle formed by projecting a point onto the sides of a triangle or their extensions is a pedal triangle.

Let ABC be a triangle, P a point, and A'B'C' the corresponding pedal triangle. Then

2

AC'

+

2

BA'

+

2

CB'

=C'

2

B

+A'

2

C

+B'

2

A

.