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 \(=\) \(\sqrt{2}\) \(cm^2\)