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Point O is the circumcenter of triangle ABC. The distance between O and Line AC is 7, and the distance between  O  and  Line AB is 15. If AC=48, what is AB?

 Nov 9, 2019
 #2
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OD   = 7

 

Since O  is the circumcenter, OD  is a perpendicular bisector  of  AC

 

So  DA  = (1/2) 48  = 24

 

And  OA  = sqrt ( OD^2  +  DA^2)   =  sqrt (7^2 + 24^2)  = sqrt (625)   =  25 

 

So triangle  OAD   is a  7 - 24 - 25  right triangle

 

And OE  =  15    and is also a perpendicular bisector of side AB

 

So triangle OAE  is a right triangle

 

And  EA  = sqrt  ( OA^2  - OE^2)  =  sqrt  ( 25^2  - 15^2)  =  sqrt (400)  =  20

 

And AB  is twice EA  =   40

 

 

cool cool cool

 Nov 9, 2019

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