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

 Apr 16, 2022
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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)

 Apr 16, 2022

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