+27 Triangle ABC has circumcenter O. If AB=10 and [OAB] = 30, find the circumradius of triangle ABC.
+129850 [ 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)
