Triangle ABC is right-angled at C, a = |BC|, b = |CA|, with a < b.
Squares ABDE, BCFG, and CAHI are erected externally to triangle ABC.
Lines HE and DG intersect at P, lines DG and FI intersect at Q, and lines FI and HE intersect at R.

If triangle PQR is right-angled, determine the value of b/a.

Animating point A until angle GQF = 89.99997°, leads to b/a = 1.41421 and its square 2.00000, so the answer is sqrt(2).

Posted by Charlie on 2010-01-22 14:12:20