What is the area of the largest triangle that can be fit in a circle of radius 12?

An equilateral triangle that can fit in a circle has the
largest area of all triangles that can be placed in a
circle.

Now for an equilateral triangle with sides a, the
area is given by (sqrt 3 / 4)*a^2

The radius of the
circumscribed circle is a / sqrt 3.

Now we have a circle of
radius 12.

Therefore a / sqrt 3 =
12

=> a = 12 * sqrt
3

Now the area of a triangle with side 12/ sqrt 3
is

=> (sqrt 3 / 4)*(12 * sqrt 3)
^2

=> (sqrt 3 / 4)* (144 *
3)

=> (144*sqrt 3* 3/
4)

=> 108*sqrt
3

The area of the largest triangle that can
be inscribed in a circle of radius 12 is 108*sqrt
3.