Area of Isosceles Triangle Given Radius & Altitude

[studof09]

A circle has a radius of 5 and the circle is circumscribed around an isosceles triangle. If the length of the altitude to the base of the triangle is 9, what is the area of the triangle?

I tried to figure out the two equal sides of the triangle by using the law of sines but you cannot assume that you have two 45 degree angles and a 90 degree angle in the two triangles split apart by the altitude. I feel like I need to know one of the angles to solve this problem.

 

[slider142]

Consider the radii of the circle and how they interact with the height of the triangle and the vertices.