Triangle ABC has circumcenter O. If AB = 10 and [OAB] = \(50\) find the circumradius of triangle ABC.

Guest Apr 16, 2022

#1**0 **

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( 50^{o} ) = 5 / AO ---> AO = 5 / cos(50^{o})

geno3141 Apr 16, 2022