Answer to Question #26483 in Geometry for kanishka

Question

ABC is an isosceles triangle with AB=BC. The circumcircle of ABC has radius 8. Given further that AC is a diameter of the circumcircle, what is the area of triangle ABC?

Answer 1

Since AC is the diameter of the circle,

AC = 16 units.

Let O be the centre of the circle, and connect O with A.
Now we get,

AO = 8 units (radius of the circle).

We know that the area of a triangle

A = 1/2 · base length(b) · height(h) [or simply 1/2·b·h].

Here base length (b) is 16 units and height (h) is 8 units. So, Area of triangle ABC is

A = 1/2·b·h = 1/2·16·8 = 64 units.