Question
Wed January 04, 2012 By:
 

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

Expert Reply
Wed January 04, 2012
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

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