BTW, how do you solve 96?

I thought that P was the first Brocard point, and did a MASSIVE coordinate bash, and I got it wrong...was it actually the first Brocard point?

Or did I make a computation mistake?

Hm...?

And I made a computation mistake on 98 too....

Outline of solution...

1.Prove that if E is the midpoint of AB, F is the midpoint of BC, G is the midpoint of CD, and H is the midpoint of DA, then I is the intersection of EG and FH. Using Mean Similiarty.

2. Notice that I is the midpoint of EG and teh midpoint of FH by Mean Similarty.

3.Show that m<AH = m< BHG.

4. Now we can easily the points where the incircle is tangent to the sides.

5. TRIG BASH!!!

And I got 9/sqt{101},
which is not right. Maybe I made a computation mistake? Hmm....