If an isosceles triangle \(ABC\), in which \(AB = AC = 6 \ cm\), is inscribed in a circle of radius \(9 \ cm\), find the area of the triangle.
 
Solution:
 
Consider \(\Delta ABO\) and \(\Delta ACO\),
 
\(AB = AC\) (given)
 
\(BO = CO\) (radii of same circle)
 
\(AO = AO\) (common)
 
Thus, by congruence rule\(\Delta ABO \cong \Delta ACO\)
 
\(angle AMB =\) \(^\circ\)
 
Area of the triangle \(=\) \(\sqrt{2}\) \(cm^2\)