Two parallel chords, 104 cm and 120 cm long, are drawn in the circle, and the distance between

Two parallel chords, 104 cm and 120 cm long, are drawn in the circle, and the distance between them is 64 cm. Find the radius of the circle.

A circle is a figure consisting of all points of the plane, for each of which the ratio of the distances to two given points is equal to a given number other than one.

Segment KН = KO + NO = 64 cm.

Let KO = X cm, then HO = (64 – X).

Let’s finish the radii of the OС and OC.

The segments KO and HO are perpendicular to the chords AB and SD, and therefore, divide them in half, then СK = СD / 2 = 120/2 = 60 cm, AH = AB / 2 = 104/2 = 52 cm.

In a right-angled triangle РНC, CO ^ 2 = CK ^ 2 + KO ^ 2 = 3600 + X ^ 2.

In a right-angled triangle AOH, OA ^ 2 = AH ^ 2 + HO ^ 2 = 2704 + (64 – X) ^ 2.

CO ^ 2 = OA ^ 2, then: 3600 + X ^ 2 = 2704 + (64 – X) ^ 2.

3600 + X ^ 2 = 2704 + 4096 – 128 * X + X ^ 2.

128 * X = 3200.

X = KO = 3200/128 = 25 cm.

Then CO^2 = 3600 + 625 = 4225.

CO = R = 65 cm.

Answer: The radius of the circle is 65 cm.