End A of line segment AB lies in the alpha plane. Parallel straight lines are drawn through the end B

End A of line segment AB lies in the alpha plane. Parallel straight lines are drawn through the end B and point C of this segment, which intersect the alpha plane, respectively, at points B1 and C1. Find the length of the segment CC1 if BB1 = 16cm and AC: BC = 3: 5.

Let us prove that triangle ABB1 is similar to triangle ACC1.

The angle A for triangles is common, the segments CC1 and BB1 are parallel by condition, then ygo ABB1 = ACC1 as the corresponding angles at the intersection of parallel CC1 and BB1 secant AB.

Then triangles ACC1 and ABB1 are similar in two angles.

Let AC = 3 * X cm, BC = 5 * X cm, then AB = 8 * X cm.

AB / AC = BB1 / CC1.

CC1 = AC * BB1 / AB = 3 * X * 16/8 * X = 6 cm.

Answer: The length of the segment CC1 is 6 cm.