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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**+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)

CPhill Nov 4, 2018