Sunday, September 20, 2009

Equilateral triangle in a circle

Let ABC be an equilateral triangle inscribed in a circle, and P a point on the arc AB. Find |CP| given that |AP|=3 and |BP|=4.
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  1. DavidSeptember 20, 2009 at 6:59 PM

    Answer: 7.

    By Ptolemy's theorem, |AC|*|BP| + |BC|*|AP| = |AB|*|CP|. Since |AC|=|BC|=|AB|, it follows that |BP|+|AP|=|CP|.

    http://www.cut-the-knot.org/proofs/ptolemy.shtml

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