Let be an acute-angled triangle such that , let be the circumcenter of triangle , and let . Denote by and the circumcenters of triangles and , respectively. Let be a point on the extension of the segment beyound such that , and let be a point on the extension of the segment beyound such that . Prove that the quadrilateral is a rectangle if and only if .
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Official version Let be the circumcenter of an acute-angled triangle with . The line meets the side at . The circumcenters of the triangles and are and , respectively. Extend the sides and beyond , and choose on the respective extensions points and such that and . Prove that the quadrilateral is a rectangle if and only if .
Edited by orl.
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Official version Let be the circumcenter of an acute-angled triangle with . The line meets the side at . The circumcenters of the triangles and are and , respectively. Extend the sides and beyond , and choose on the respective extensions points and such that and . Prove that the quadrilateral is a rectangle if and only if .
Edited by orl.