Finding the Diameter of a Cyclic Quadrilateral

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Homework Statement


Given a cyclic quadrilateral with side lengths 1, 2, 3 and d (in that order) where d is the diameter of the circle, find d.


The Attempt at a Solution



I tried using Ptolemy's theorem and Brahmagupta's formula, but to no avail. Can I get pointed in the correct direction please?
 
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Maybe you can find something useful http://pballew.blogspot.com/2009/10/notes-on-cyclic-quadrilaterals.html" .
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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