Cyclic Crossed Pentagon Problem

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Given a cyclic crossed (or star) pentagon as show below with B the midpoint of arc AC, what relationship do you notice between linesegments AC and XY? Drag any of the red vertices to explore and make a conjecture.

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Cyclic Crossed Pentagon Problem

Can you explain why (prove that) your conjecture is true?

Note: this problem is a generalization of Student Problem 2013.3 from the Mathematical Gazette, 97(540), Nov 2013, p. 552.

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By Michael de Villiers. Created, 3 May 2014.