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Indian RMO- Paper -3

Source: RMO Problem 3

December 11, 2013
geometryperpendicular bisectorgeometry unsolved

Problem Statement

In an acute-angled triangle ABCABC with AB<ACAB < AC, the circle ω\omega touches ABAB at BB and passes through CC intersecting ACAC again at DD. Prove that the orthocentre of triangle ABDABD lies on ω\omega if and only if it lies on the perpendicular bisector of BCBC.
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