In a circle with a radius of 10 cm, two parallel chords are drawn on opposite sides of the center

| May 11, 2021 | education

In a circle with a radius of 10 cm, two parallel chords are drawn on opposite sides of the center with a length of 12 cm and 16 cm. find the distance between them.

Draw a segment BE through the center of the circle O, perpendicular to two parallel chords AC = 16 cm and FD = 12 cm. We connect the center of the circle with points C and D. Two right-angled triangles are formed, the hypotenuses of which OC and OD are equal to the radius of the circle R = 10 cm, and the legs are equal to half the lengths of the chords: BC = AC / 2 = 8 cm, ED = FD / 2 = 6 cm.

The distance between the chords will be equal to the segment BE, which is equal to the sum of the legs OE and OB of triangles OED and OBC:

OE = OB + OE = √ (R ^ 2 – ED ^ 2) + √ (R ^ 2 – BC ^ 2) = √ (100-36) + √ (100-64) = 8 + 6 = 14 cm.

Answer: 14 cm.



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