In the triangle MNC, the points Q and P are marked on the sides NC and MC, so that NQ = QC and MP = PC.

In the triangle MNC, the points Q and P are marked on the sides NC and MC, so that NQ = QC and MP = PC. Find PQ if AB = 8 and MN is the midline of triangle ABC parallel to AB

Since MN is the middle line of the triangle ABC, then MN = AB / 2 = 4;

Likewise, the MNC triangle is similar to the PQC triangle: because they have a common angle C and the QC side refers to the NC side, just as PC refers to the MC.

This implies that QP is parallel to MN. QP also divides the sides NC and MC in half, which means QP is the midline of triangle MNC and equals half of MN: QP = 4/2 = 2.

Answer: QP = 2.