MathDB

There are 3 lines

r, s

and

t

on a plane. The lines

r

and

s

intersect perpendicularly at point

A

. the line

t

intersects the line

r

at point

B

and the line

s

at point

C

. There exist exactly 4 circumferences on the plane that are simultaneously tangent to all those 3 lines.
Prove that the radius of one of those circumferences is equal to the sum of the radius of the other three circumferences.

Problem Statement