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-

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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