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Question Number 70298 by naka3546 last updated on 03/Oct/19

	Answered by mr W last updated on 03/Oct/19

	Commented by mr W last updated on 03/Oct/19

	$C E = \sqrt{{(x + 1)}^{2} - x^{2}} = \sqrt{2 x + 1}$ $\frac{C E}{E D} = \frac{C A}{A B}$ $\Rightarrow \frac{\sqrt{2 x + 1}}{x} = \frac{2 x + 1}{12}$ $\Rightarrow \frac{1}{x} = \frac{\sqrt{2 x + 1}}{12}$ $\Rightarrow x \sqrt{2 x + 1} = 12$ $\Rightarrow x^{2} (2 x + 1) = 144$ $\Rightarrow 2 x^{3} + x^{2} - 144 = 0$ $\Rightarrow (x - 4) (2 x^{2} + 9 x + 36) = 0$ $\Rightarrow x = 4$ $\Rightarrow d i a m e t e r = 8$
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