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right-angle triangle ABC

Source: China south east mathematical Olympiad 2007 problem 6

July 12, 2013
geometrycircumcirclecyclic quadrilateralgeometry unsolved

Problem Statement

In right-angle triangle ABCABC, ∠C=90\angle C=90°, Point DD is the midpoint of side ABAB. Points MM and CC lie on the same side of ABAB such that MB⊥ABMB\bot AB, line MDMD intersects side ACAC at NN, line MCMC intersects side ABAB at EE. Show that ∠DBN=∠BCE\angle DBN=\angle BCE.
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