The segments AB and CM intersect at point O so that AC II BM. Find the length of the segment CM if AC = 15 cm, BM = 3 cm, CO = 10 cm.

Consider triangles MBO and AOC:
1.The angle of the MOВ is equal to the angle of the AOC, as is the vertical.
2. the angle OAС is equal to the angle OBM as internal one-sided with parallel straight lines.
3. The angle of the OCA is equal to the angle of OMB as internal one-sided with parallel straight lines.
The MВO triangle is similar to the OAC triangle in three corners.

So we can make a proportion:
10/15 = OM / 3
ОМ = 30/15
ОМ = 2

Find MС:
10 + 2 = 12 cm
Answer: MС = 12 cm