In a convex quadrilateral $ABCD$, $\angle ABC = 90^o$ , $\angle BAC = \angle CAD$, $AC = AD, DH$ is the alltitude of the triangle $ACD$. In what ratio does the line $BH$ divide the segment $CD$?
Problem
Source: 2003 Oral Moscow Geometry Olympiad grade 9 p2
Tags: ratio, geometry, right angle, equal segments, equal angles