Image via Wikipedia

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.