1. The problem statement, all variables and given/known data Let ABC be a right angled triangle such that A=90, AB=AC and let M be the mid point of the side AC. Take the point P on the side BC so that AP is vertical to BM. Let H be the intersection of AP ad BM. Find the ratio BP : PC. 2. Relevant equations AB=AC AM = MC BP : PC = ? See the problem here: http://4.bp.blogspot.com/_Qc1Z3hIcYO4/SgbXNoa555I/AAAAAAAABPM/ruupwSz5EoE/s1600-h/bp_pc.JPG. 3. The attempt at a solution I drew parallel lines, and I found some interesting connections. I am very close to the answer, but I still cannot find it. Please, see the attachment "parallel_lines.jpg".