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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
Aquadrilateralwithconsecutivesidesoflenght7,15,15,anddisinscribedinacirclewithitsdiameterd.Findtheradiusofcircle
Answered by ajfour last updated on 31/Mar/17
Commented by ajfour last updated on 31/Mar/17
AB=7 ;    BC=15;   CD=15;  AD= d =2r  OM= (7/2)   midpoint theorem.  CM= (r−(7/2))  ;    DM= ((√(4r^2  −49))/2)  CM^2  + DM^2  = CD^2   (r−(7/2))^2 + (((4r^2  −49)/4)) = 225  2r^2 −7r −225 =0  r =((7±(√(49+1800)))/4)  and as r>0 ,  r= ((7+43)/4) = ((25)/2) .
AB=7;BC=15;CD=15;AD=d=2rOM=72midpointtheorem.CM=(r72);DM=4r2492CM2+DM2=CD2(r72)2+(4r2494)=2252r27r225=0r=7±49+18004andasr>0,r=7+434=252.
Commented by Joel576 last updated on 31/Mar/17
thank you very much
thankyouverymuch
Commented by Joel576 last updated on 01/Apr/17
but how did you know that point C, M, O  in one line ?
buthowdidyouknowthatpointC,M,Oinoneline?
Commented by ajfour last updated on 01/Apr/17
△CBD is isosceles so perpendicular  from C on BD bisects it.A line   perpendicular to BD from center  of circle even bisects its chord BD.
CBDisisoscelessoperpendicularfromConBDbisectsit.AlineperpendiculartoBDfromcenterofcircleevenbisectsitschordBD.
Commented by mrW1 last updated on 01/Apr/17
what′s the result if the sides are 15,7,15 and d?
whatstheresultifthesidesare15,7,15andd?
Commented by ajfour last updated on 01/Apr/17
the same.
thesame.

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