Establish a polar coordinate, with m as the origin of the X axis, and the X axis is parallel to the BC side. Let the radius of a circle be R. So the coordinates of m are (rcos@, rsin@), A(0, r), B(- root number 3/2*r,-1/2*r)C(- (root number 3)/2*r,-1.
│MA│^2=(rcos@)^2+(rsin@-r)^2
│MB│2 =(rcos @++radical 3/2 * r) 2+(rsin @+ 1/2 * r) 2
│MC│2 =(rcos @- radical 3/2 * r) 2+(rsin @+ 1/2 * r) 2
Ordered: │ Ma │ 2+│ MB │ 2+│ MC │ 2 = 6r 2.
Use your hands completely, and you will see.