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concyclic lead to concyclic (Greece Junior 2019)

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July 15, 2019
geometryConcycliccyclic quadrilateralcircumcircle

Problem Statement

Let ABCDABCD be a quadrilateral inscribed in circle of center OO. The perpendicular on the midpoint EE of side BCBC intersects line ABAB at point ZZ. The circumscribed circle of the triangle CEZCEZ, intersects the side ABAB for the second time at point HH and line CDCD at point GG different than DD. Line EGEG intersects line ADAD at point KK and line CHCH at point LL. Prove that the points A,H,L,KA,H,L,K are concyclic, e.g. lie on the same circle.
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