In a regular triangular pyramid SABC with vertex S, all edges of which are equal to 2, point M

In a regular triangular pyramid SABC with vertex S, all edges of which are equal to 2, point M is the midpoint of edge AB, point O is the center of the pyramid base, point F divides the SO segment in a ratio of 3: 1, counting from the top of the pyramid. Find the distance from point C to line MF.

It is necessary to find the distance from C to the straight line MF, and this is the perpendicular drawn from the point to the straight line, in this case CК. He must be found.
Because O is the center of the base, then the SO is the height of the pyramid, and it is perpendicular to the plane of the base, which means that the angle SOC = 90 degrees.
Is the SOC triangle similar to the MKC triangle? then the Kgol SCM is also 90 degrees.
From the similarity of the triangles, the aspect ratio MC: SC = KC: OC follows.
OC = 2 / 3MC
MC = root (4-1) = root of 3 (by the Pythagorean theorem)
means OS = 2/3 * root of 3
KS = (MC * OC) / SC = 1