In a circle with a radius of 25 cm, 2 parallel chords are drawn. The lengths of which are 40 and 30cm.

| May 29, 2021 | education

In a circle with a radius of 25 cm, 2 parallel chords are drawn. The lengths of which are 40 and 30cm. Find the distance between them.

Draw the radii of the circle to the edges of the chords. ОА = ОВ = ОВ = ОD = 25 cm.

Triangles AOB and COD are isosceles, then the heights OK and OH are also their medians, then AK = ВK = AB / 2 = 30/2 = 15 cm.

CH = DH = CD / 2 = 40/2 = 20 cm.

By the Pythagorean theorem, we determine the lengths of the heights of the OC and OH.

OK ^ 2 = OA ^ 2 – AK ^ 2 = 625 – 225 = 400.

OK = 20 cm.

OH ^ 2 = OC ^ 2 – CH ^ 2 = 625 – 400 = 225.

OH = 15 cm.

Then KH = OH + OK = 15 + 20 = 35 cm.

If the chords are located on one side of the center of the circle, then KН = OK – OH = 20 – 15 = 5 cm.

Answer: The distance between the chords is 35 cm or 5 cm.



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