The Product of the Perpendiculars to the Sides of a Triangle

rotate P

PD	≈	4.02	PE	≈	2.53	PF	≈	1.76
PR	≈	1.11	PS	≈	2.80	PT	≈	5.79

PD

×

PE

×

PF

≈

17.90

PR

×

PS

×

PT

≈

17.90

The tangential triangle of a triangle ABC is the triangle (A'B'C' in the figure) formed by the tangents to the circumcircle of ABC at A, B, and C.

The product of the distances from a point P on the circumcircle of a triangle ABC to its sides equals the product of the distances of P to the sides of the tangential triangle A'B'C':

PE×PF×PG=PR×PS×PT

.