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Locus of orthocentre of triangle ABP

Source: ITAMO 2006 Q3

May 8, 2006
geometrygeometric transformationreflectionparallelogramcomplex numbersgeometry proposed

Problem Statement

Let AA and BB be two distinct points on the circle Γ\Gamma, not diametrically opposite. The point PP, distinct from AA and BB, varies on Γ\Gamma. Find the locus of the orthocentre of triangle ABPABP.
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