Geometry Puzzle

Below, you find a nice geometry puzzle.
If you can solve it send your solution , with your name and e-mail address, to

D.E.Dirkse
Brederodestraat 28
1901HW Castricum
the Netherlands

or to

de.dirkse@hccnet.nl

so I can publish it here.

Description
Given are:
- a circle with radius r₁ and inside
- two circles with radius r₂ and r₃ which contact circle 1 at points A and B
- the centers of circles 1,2 and 3.
- the intersection point P of circles 2 and 3

Prove the following theorem:

If P is on line AB then r₁ = r₂ + r₃ must be true

success...!

---

OneStat