If an isosceles triangle ABC in which AB=AC=6cm is inscribed in a circle of radius 9cm. Find the area of the triangle.

Let AM = x cm

In quadrilateral OBAC, OB = OC = 9 cm and AB = AC = 6 cm

Thus, OBAC is a kite. It is known that the diagonals of a kite are perpendicular to each other.

Therefore OA perpendicular to BC

In right angled triangle AMC,

AM² + MC² = AC² [Pythagoras theorem]

therefore, MC² = (6² – x²) cm²

 

Using Pythagoras theorem for triangle OMC, it is obtained

OM² + MC² = OC²

implies (9 – x)² + (6² – x²) = 9²

implies 81 + x² – 18x + 36 – x² = 81

implies 18x = 36

implies x = 2