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Question Number 174283 by ajfour last updated on 28/Jul/22

Commented by ajfour last updated on 28/Jul/22

$F i n d P Q i n t e r m s o f a, b, θ .$
	Answered by mr W last updated on 29/Jul/22

	$A = c e n t e r o f c i r c l e a$ $B = c e n t e r o f c i r c l e b$ $P Q = 2 r$ $A B = \frac{b - a}{\sin \frac{θ}{2}} = d$ $d = \sqrt{a^{2} - r^{2}} + \sqrt{b^{2} - r^{2}}$ $d^{2} + a^{2} - r^{2} - 2 d \sqrt{a^{2} - r^{2}} = b^{2} - r^{2}$ $d^{2} + a^{2} - b^{2} = 2 d \sqrt{a^{2} - r^{2}}$ ${(d^{2} + a^{2} - b^{2})}^{2} = 4 d^{2} (a^{2} - r^{2})$ $r = \sqrt{a^{2} - {(\frac{d^{2} + a^{2} - b^{2}}{2 d})}^{2}}$ $\Rightarrow P Q = 2 \sqrt{a^{2} - {(\frac{d^{2} + a^{2} - b^{2}}{2 d})}^{2}}$
	Commented by ajfour last updated on 29/Jul/22

	$w o n d e r f u l, t h a n k s S i r!$
	Commented by Tawa11 last updated on 29/Jul/22

	$Great sir$
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