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Question Number 52198 by ajfour last updated on 04/Jan/19

	Answered by MJS last updated on 04/Jan/19

	$c_{1} : x^{2} + y^{2} = 4 R^{2}$ $c_{2} : x^{2} + {(y - R)}^{2} = R^{2}$ $c_{3} : {(x - q)}^{2} + {(y - r)}^{2} = r^{2}$ $now intersect c_{1} \cap c_{3} and c_{2} \cap c_{3} with exactly$ $one solution each$ $\Rightarrow q = \sqrt{2} R, r = \frac{1}{2} R$
	Commented by ajfour last updated on 04/Jan/19

	$o k a y S i r, t h a n k s f o r A n s w e r, i$ $s h a l l t r y s o l v i n g .$
	Answered by mr W last updated on 04/Jan/19

	Commented by ajfour last updated on 04/Jan/19

	$W o n d e r f u l S i r!$
	Commented by mr W last updated on 04/Jan/19

	${(R + r)}^{2} - {(R - r)}^{2} = {(2 R - r)}^{2} - r^{2}$ $4 R r = 4 R (R - r)$ $\Rightarrow \frac{R}{r} = 2$
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