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

Asked by manoj gokikar | 26th Feb, 2011, 02:38: PM

Expert Answer:

Dear Student,
Here is the solution:
The given information can be represented using a figure as:
 
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.
∴ OA ⊥ BC
 In right angled ∆AMC,
AM2 + MC2 = AC2   [Pythagoras theorem]
⇒ MC2 = (62x 2) cm2
 
Using Pythagoras theorem for ∆OMC, it is obtained
OM2 + MC2 = OC2
⇒ (9 – x)2 + (62x 2) = 92
⇒ 81 + x 2 – 18x + 36 – x 2 = 81
⇒18x = 36
x = 2
Regards
Team Topperlearning

Answered by  | 26th Feb, 2011, 12:43: PM

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