In an isosceles triangle ABC, base AC = 16 cm, side AB = 18 cm. Points P and K are marked on sides AB

In an isosceles triangle ABC, base AC = 16 cm, side AB = 18 cm. Points P and K are marked on sides AB and BC so that PK || AC, PK = 12 cm. Find the length of the segment BK.

Let us prove that triangles ABC and PBK are similar. The angle ABC in triangles is common, the angle BAC is equal to the angle of the BPK as the corresponding angles at the intersection of parallel straight lines AC and РK secant AB, then triangles ABC and PBM are similar in two angles.

Since the triangle ABC is isosceles, then BC = AB = 18 cm

In such triangles, RK / AC = BK / BC.

12/16 = BK / 18.

BK = 12 * 18/16 = 13.5 cm.

Answer: The length of the segment BK is 13.5 cm.