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Orthocenter of variable triangles

Source: BdMO 2023 Higher Secondary National P4

February 12, 2023
geometryorthocenter

Problem Statement

Let ABCDABCD be an isosceles trapezium inscribed in circle ω\omega, such that AB∣∣CDAB||CD. Let PP be a point on the circle ω\omega. Let H1H_1 and H2H_2 be the orthocenters of triangles PADPAD and PBCPBC respectively. Prove that the length of H1H2H_1H_2 remains constant, when PP varies on the circle.
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