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

Make a sketch, and join the vertices of the isosceles triangle to the centre of the circle. You'll notice that you now have 3 triangles, two of which are similar and one other triangle.

You can find the angles AOC, AOB and BOC, where O is the centre of the triangle, making use of the cosine rule. Once you get the angles, you can find the area using the formula:

Area = \frac12 ab\ \sin \hat{c}

The given information can be represented using a figure as:

http://www.meritnation.com/app/webroot/img/userimages/mn_images/image/04Feb2011-1-i.png
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]
â‡' MC2 = (62 – x 2) cm2

Using Pythagoras theorem for ∆OMC, it is obtained
OM2 + MC2 = OC2
â‡' (9 – x)2 + (62 – x 2) = 92
â‡' 81 + x 2 – 18x + 36 – x 2 = 81
â‡'18x = 36
â‡'x = 2
http://www.meritnation.com/app/webroot/img/userimages/mn_images/image/04Feb2011-1-iI.png