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CD = 2 OF , cyclic ABCD with _|_ diagonals

Source: 2022 Austrian Federal Competition For Advanced Students, Part 1 p2

October 4, 2022
geometrycyclic quadrilateralequal segments

Problem Statement

The points A,B,C,DA, B, C, D lie in this order on a circle with center OO. Furthermore, the straight lines ACAC and BDBD should be perpendicular to each other. The base of the perpendicular from OO on ABAB is FF. Prove CD=2OFCD = 2 OF.
(Karl Czakler)
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