A quadrilateral with consecutive sides of lenght 7, 15, 15, and d is inscribed in a circle with its diameter d. Find the radius of circle


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Question Number 11759 by Joel576 last updated on 31/Mar/17

$A quadrilateral with consecutive sides of lenght 7, 15, 15, and d$ $is inscribed in a circle with its diameter d .$ $Find the radius of circle$
	Answered by ajfour last updated on 31/Mar/17

	Commented by ajfour last updated on 31/Mar/17

	$A B = 7; B C = 15; C D = 15;$ $A D = d = 2 r$ $O M = \frac{7}{2} m i d p o i n t t h e o r e m .$ $C M = (r - \frac{7}{2}); D M = \frac{\sqrt{4 r^{2} - 49}}{2}$ ${C M}^{2} + {D M}^{2} = {C D}^{2}$ ${(r - \frac{7}{2})}^{2} + (\frac{4 r^{2} - 49}{4}) = 225$ $2 r^{2} - 7 r - 225 = 0$ $r = \frac{7 \pm \sqrt{49 + 1800}}{4} a n d a s r > 0,$ $r = \frac{7 + 43}{4} = \frac{25}{2} .$
	Commented by Joel576 last updated on 31/Mar/17

	$t h a n k y o u v e r y m u c h$
	Commented by Joel576 last updated on 01/Apr/17

	$but how did you know that point C, M, O$ $in one line ?$
	Commented by ajfour last updated on 01/Apr/17

	$△ C B D i s i s o s c e l e s s o p e r p e n d i c u l a r$ $f r o m C o n B D b i s e c t s i t . A l i n e$ $p e r p e n d i c u l a r t o B D f r o m c e n t e r$ $o f c i r c l e e v e n b i s e c t s i t s c h o r d B D .$
	Commented by mrW1 last updated on 01/Apr/17

	${w h a t}^{'} s t h e r e s u l t i f t h e s i d e s a r e 15, 7, 15 a n d d ?$
	Commented by ajfour last updated on 01/Apr/17

	$t h e s a m e .$
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