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Triangle ABC has circumcenter O. If AB = 10 and the area of OAB is 30, find the circumradius of triangle ABC.
 

 Nov 7, 2019
edited by mathleteig  Nov 7, 2019
edited by mathleteig  Nov 7, 2019
 #1
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Circumradius = 2*30/10 = 6.

 Nov 7, 2019
 #2
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We can let A  = (0,0)

And B  = (10, 0)

Since [ OAB ] = 30....then  we can let O be (5, 6)

 

The distance between  O  and any vertex  is   sqrt  (5^2 + 6^2)  =  sqrt (61)  =  circumradius

 

So C  must be   ( 5, 6 + sqrt (61) )

 

See the image, here : 

 

 

cool cool cool

 Nov 7, 2019

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