In a circle with a radius of 65 cm, two parallel chords A1B1 and A2B2 are drawn, respectively equal

| June 21, 2021 | education

In a circle with a radius of 65 cm, two parallel chords A1B1 and A2B2 are drawn, respectively equal to 126 cm and 112 cm. Find the distance between the chords.

Through point O, the center of the circle, draw perpendiculars to the chords. The segment OP divides the chord A1B1 in half, then PA1 = PB1 = A1B1 / 2 = 126/2 = 63 cm.

The segment OK divides the chord A2B2 in half, then KA ^ 2 = KB ^ 2 = A2B2 / 2 = 112/2 = 56 cm.

In a right-angled triangle OB1R, according to the Pythagorean theorem, OP ^ 2 = OB1 ^ 2 – PB1 ^ 2 = 4225 – 3969 = 256. OP = 16 cm.

In a right-angled triangle OKВ2, according to the Pythagorean theorem, OK ^ 2 = OB2 ^ 2 – KB2 ^ 2 = 4225 – 3136 = 1089. OK = 33 cm.

Then РK = OР + OK = 16 + 33 = 49 cm.

Answer: The distance between the chords is 33 cm.



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