Through the point of intersection of the medians of the MRK triangle, a segment of CD

Through the point of intersection of the medians of the MRK triangle, a segment of CD, parallel to the MC, CD = 18 cm, is drawn. Find MK?

The intersection of the medians divides the medians into a 1: 2 ratio.
According to Thales’ theorem, the sides are divided by the segment СD in the same ratio CM – 1, СР – 2 if MP – 3.
From the condition of similarity of triangles СDР and MKР
СD: MK = СР: MP = 2: 3
MK = СD * 3/2 = 18 * 3/2 = 27 cm
Answer: MK = 27cm