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Problem 1 vietnamese tst 2006

Source: Vietnamese TST 2006

April 17, 2006
geometrycircumcircletrigonometryparallelogramratiogeometry proposed

Problem Statement

Given an acute angles triangle ABCABC, and HH is its orthocentre. The external bisector of the angle ∠BHC\angle BHC meets the sides ABAB and ACAC at the points DD and EE respectively. The internal bisector of the angle ∠BAC\angle BAC meets the circumcircle of the triangle ADEADE again at the point KK. Prove that HKHK is through the midpoint of the side BCBC.
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