Segment KM and FM diameters of a circle centered at point O. Prove that a) angle FEM = KME b) KE = MF

Apparently, there is a typo in the condition and the second diameter is FE.
According to the condition KM and FE are diameters, point O is the center of the circle, then:
ОМ = OK = OF = OE – the radii of the circle.
a) Consider a triangle MOE, in which:
ОМ = ОЕ, which means that the triangle is isosceles, the radii are the sides.
The angles at the base are equal:
∠ FEM = ∠ KME.
Q.E.D.
b) Consider triangles KOE and MOF.
In them:
ОМ = OK = OF = OE;
∠ KОЕ = ∠ MOF (vertical).
The triangles are equal in the first place.
Therefore, KE = MF.
What was required to prove.