You can put this solution on YOUR website! Connecting the center of the inscribed circle to the vertices,
and to the midpoints of the sides,
divides the equilateral triangle into
three congruent isosceles triangles,
three congruent kites,
six congruent right triangles,
all of them with the center of the circle for a vertex.
I drew some of that below. In the red triangle .
Since , .