In a cylinder with radii OC and OC1 equal to 5, height 15, point D is taken on the circle of radius OC, C1D = 17.

| September 3, 2021 | education

In a cylinder with radii OC and OC1 equal to 5, height 15, point D is taken on the circle of radius OC, C1D = 17. Find the distance between straight lines C1D and OO1.

Let’s determine the length of the chord СD, which is the leg of the right-angled triangle С1СD. CD ^ 2 = C1DD ^ 2 – CC1 ^ 2 = 289 – 225 = 64.

CD = 8 cm.

Let’s draw the radii of the OC and OD. The OCD triangle is isosceles, then the OH height is also the median of the triangle, then CH = DH = CD / 2 = 8/2 = 4 cm.

The distance between the segment C1D and OO1 is the segment KP.

С1Д lies on the plane С1СДД1, as well as the segment СD, then the segment ОН is also the shortest distance between С1D and OO1.

OH ^ 2 = OC ^ 2 – CH ^ 2 = 25 – 16 = 9.

OH = 3 cm.

Answer: The distance between straight lines C1D and OO1 is 3 cm.



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