Two points that lie on the circles of different bases of the cylinder are connected by a segment.

Two points that lie on the circles of different bases of the cylinder are connected by a segment. Find its length if the radius is 10 cm, the height is 17 cm, and the distance from the axis to the segment is 4 cm.

Let point A lie on the upper circle of the base, point B lies on the lower circle of the base, O is the center of the lower circle.

Let’s find the length AB.

Points A and B are located so that if they were located on the same circle, they would be on opposite sides of the radius.

Point A will be projected onto the lower base.

We get a segment AA1 equal to the height of the cylinder, triangle A1AB is rectangular.

The chord A1B is located from the axis at a distance OH = 4 cm, where OH is the height of an isosceles triangle A1OB with sides AO = OB = r = 10 cm.

Then A1B = 2 * HB.

From right triangle НОВ:

HB ^ 2 = OB ^ 2 – OH ^ 2 = 100 – 16 = 84 cm ^ 2.

A1B ^ 2 = 4 * HB ^ 2 = 4 * 84 = 336 cm ^ 2.

From the triangle A1AB by the Pythagorean theorem we find AB.

AB ^ 2 = (AA1) ^ 2 + (A1B) ^ 2 = 17 ^ 2 + 336 = 289 + 336 = 625 cm ^ 2.

AB = 25 cm.