In a circle with a radius of 25 cm, two parallel chords are drawn on opposite

In a circle with a radius of 25 cm, two parallel chords are drawn on opposite sides of the center, 40 and 30 cm. Find the distance between them.

Let’s draw the radii of the circle to points A, B, C, D. OA = OB = OS = OD = 25 cm.

Then triangles AOB and COD are isosceles. The heights of OK and OH are also the medians of the triangles, then AK = VK = 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.

Answer: The distance between the chords is 35 cm.