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ratio chasing, <ABC = 90^o , <BAC =<CAD, AC = AD, DH altitude

Source: 2003 Oral Moscow Geometry Olympiad grade 9 p2

October 26, 2020
ratiogeometryright angleequal segmentsequal angles

Problem Statement

In a convex quadrilateral ABCDABCD, ∠ABC=90o\angle ABC = 90^o , ∠BAC=∠CAD\angle BAC = \angle CAD, AC=AD,DHAC = AD, DH is the alltitude of the triangle ACDACD. In what ratio does the line BHBH divide the segment CDCD?
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