Let ABC be a 90-degree triangle with hypotenuse BC. Let D and E distinct points on segment BC and P,Q be the foot of the perpendicular from D to AB and E to AC, respectively. DP and EQ intersect at R.
Lines CR and AB intersect at M and lines BR and AC intersect at N.
Prove that MN∥BC if and only if BD=CE. geometrysimilar trianglesnational olympiad