Proof geometrically that QX and QY are the roots

[raphael3d]

http://img717.imageshack.us/img717/4...10106at123.png

its a construction from felix klein, around 1900. it should be made without trigonometric functions or complex algebra etc.

the ratios of lengths should be sufficient, but i have only found one similar triangle and then i got stuck.

but is the best strategy to show that the lengths QX and QY are the roots?

 

[HallsofIvy]

That is a broken link.

 

[raphael3d]

excuse me sir, here is a the working link:

http://img717.imageshack.us/img717/4029/screenshot20110106at123.png

thank you