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Quadrilateral & Circle problem

medival ideal portrait of Ptolemy

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Quadrilateral ABCD is inscribed in a circle. Let AB = a, BC = b, CD = c, DA = d, AC = p and BD = q. Prove Ptolemy’s second theorem that p \cdot q = \frac{ad+bc}{ab+cd} .

This question is also taken from Bertley Math Circle .

It is easy question, just use R = \frac{abc}{4S} a, b, c are sides of triangle and S is area of triangle.

If you couldn’t prove send me mail, and i will give few tips.

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  1. October 4, 2011 at 14:13
  2. October 8, 2011 at 14:16
  3. October 31, 2011 at 11:43

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