The geometric center of an equilateral triangle is also the center of the circumscribed circle. This means that the distance from the center of the triangle to its vertex is also the same to the radius of the circle.
The translation of the problem is that you draw a triangle inside a circle.
The circle's area is 144 cm^2. To find the radius:
A of circle =pi* radius^2
radius=sqrt (144/pi)
r=6.77 approximately
If you connect the center point of the triangle to it's vertices you will make 3 isosceles triangles. The length of the sides of the isosceles triangle are 6.77,6.77 and the unknown side. Also, the line from the center to the vertex is an angle bisector (read properties of equilateral triangles). Since equilateral triangles have interior angles that measure 60° half of that is 30°. So the measurement of the obtuse angle of the isosceles triangle is 120°. (120°+30°+30°=180°)
To find the unknown side (length of the side of the triangle) use cosine law. I'll attach a picture of the solution.
