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In a circle, two parallel chords of lengths 4 and 6 centimetres are 5 centimetres apart. What is the radius of the circle?

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In a circle, two parallel chords of lengths 4 and 6 centimetres are 5 centimetres apart. What is the radius of the circle?

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Best answer

MN = 5

ON = x

OM = 5 – x

x2 + 32 = (5 – x)2 + 22

x2 + 9 = 25 – 10x + x2 + 4

9 = 25 – 10x + 4

10x = 25 + 4 – 9

10x = 20

x = 20/10 = 2

Radius = \(\sqrt{2^2+3^2}\) = \(\sqrt{4+9}\) = \(\sqrt{13}\) cm

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