Point A is marked in the MPK triangle on the MK side, point C on the PK side, and, AC || MP.

Point A is marked in the MPK triangle on the MK side, point C on the PK side, and, AC || MP. Find the length of the segment AC, if MK = 20 cm, AM = 8 cm, MR = 15 cm

By condition, AC is parallel to MP, and since a straight line parallel to the side of the triangle cuts off a similar triangle from it, the triangles PMK and ACK are similar.

Since the ratio of the similar sides of such triangles is equal, you can make an equality:

MР / AC = MK / AK.

We find the length of the AK from the condition:

AK = MK – AM = 20 – 8 = 12 cm.

Then:

AC = MР * AK / MK = 15 * 12/20 = 9 m.

Answer: AC = 9 cm.