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Question Number 156913 by cortano last updated on 17/Oct/21

	Answered by mr W last updated on 17/Oct/21

	Commented by cortano last updated on 17/Oct/21

	$b l u e l e n g t h = 10 . y e s t h a n k s$
	Commented by mr W last updated on 17/Oct/21

	$O D = \sqrt{{(R - r)}^{2} - r^{2}} = \sqrt{R (R - 2 r)}$ $F D = R + \sqrt{R (R - 2 r)} = b l u e$ $O E = O D - r = \sqrt{R (R - 2 r)} - r$ $E G = R - O E$ $F E = R + O E$ ${A E}^{2} = F E \times E G = R^{2} - {O E}^{2}$ ${F A}^{2} = {A E}^{2} + {F E}^{2} = R^{2} - {O E}^{2} + {F E}^{2}$ ${F A}^{2} = R^{2} - {O E}^{2} + {(R + O E)}^{2}$ ${F A}^{2} = 2 R^{2} + 2 R \times O E$ ${F A}^{2} = 2 R^{2} + 2 R \times [\sqrt{R (R - 2 r)} - r]$ ${F A}^{2} = R^{2} + 2 R \sqrt{R (R - 2 r)} + R (R - 2 r)$ ${F A}^{2} = {[R + \sqrt{R (R - 2 r)}]}^{2}$ $F A = R + \sqrt{R (R - 2 r)} = g r e e$ $i t i s t o s e e F D = F A, i . e . b l u e = g r e e n .$
	Commented by Tawa11 last updated on 17/Oct/21

	$great sir$
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