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

robotjeremyc  Nov 4, 2018
 #1
avatar+91213 
+1

 [ OAB]  =  30

And since AB = 10....then the altitude  of triangle  OAB  is

 

30  = (1/2) AB * altitude

60 = 10 * altitude

6 = altitude

 

And AB is a chord of the circumcircle.....and the altitude of OAB meets chord AB at right angles, so it bisects AB  ....so 1/2AB  = 5

 

And this altitude and 1/2 AB = 5   will form the legs of a right triangle with the circumradius as the hypotenuse

 

So

 

circumradius  =   sqrt  [ 6^2 + 5^2 ]   =  sqrt [ 36 + 25 ]  =  sqrt (61)

 

 

 

cool cool cool

CPhill  Nov 4, 2018
edited by CPhill  Nov 6, 2018

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