Triangle ABC has circumcenter O. If AB = 10 and [OAB] = \(50\) find the circumradius of triangle ABC.
Since O is the circumcenter, AO will be the circumradius (as will also be OB and OC).
Let X be the midpoint of AB.
Draw OX; OX will be perpendicular to AB.
Since AB = 10, AX = 5.
Triangle(AXO) will be a right triangle with right angle(AXO) and hypotenuse AO.
cos( angle(AX0) ) = 5 / AO
cos( 50o ) = 5 / AO ---> AO = 5 / cos(50o)