Locus circle and equilateral triangle question

Question

An equilateral triangle of side 25cm circumscribes a circle. Find the radius of the circle.

I drew it out, and tried to create a right angled triangle and perform Pythagoras but it was not right, do you have any idea where I went wrong? Or how to solve it?

Thank you.

Answer 1

Strong hint: The red triangle here has one vertex in the vertex of the black triangle, one vertex where the circle touches the black triangle, and one vertex at the center of the circle.

The angles in the red triangle are $30^\circ, 60^\circ$ and $90^\circ$. One of the legs is the radius of the circle, and the other leg is half the side of the black triangle.