BMO Round 1, 2010

Geometry Difficulty 6.0 National Olympiad Prove it United Kingdom

Points $A$ , $B$ , $C$ , $D$ and $E$ lie, in that order, on a circle and the lines $AB$ and $ED$ are parallel. Prove that $\angle ABC = 90^\circ$ if, and only if, $AC^2 = BD^2 + CE^2$ .

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