I was trying to come up with a rigorous proof of the reflective property of the ellipse. I decided it was a task better left to analysis. However, I did find this little curiousity. You can see the remnants of my endeavour by the point O.[br][br]If you want to prove the below, notice that if they really do have the same incircle,[math]AG+BH=AC+BC[/math]. Or try to use the fact that a line like [math]EG[/math] is equal to the sum of its two adjacent sides minus the opposite one divided by 2.