# A plane is drawn through the end A of segment AB. through the end of B and point C of this segment

A plane is drawn through the end A of segment AB. through the end of B and point C of this segment, parallel straight lines are drawn that perpendicular to the plane at points B1 and C1, find the length of the segment BB1, if CC1 = 15cm, AC: BC = 2: 3.

Since the straight lines BB1 and CC1, by condition, are parallel, they lie in the same plane. The segment BC lies in this plane, point A lies on the segment BC, then point A also belongs to this plane.

Then the intersection points A, C1, B1 lie on one straight line.

Triangles ACC1 and ABB1 are similar in two angles.

Let the length of the segment BC = 3 * X, then AC = 2 * X, AC = 5 * X.

Then the coefficient of similarity of triangles is: K = AC / AB = 2 * X / 5 * X = 2/5.

CC1 / BB1 = 2/5.

BB1 = CC1 * 5/2 = 15 * 5/3 = 37.5 cm.

Answer: The length of the segment BB1 is 37.5 cm.

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