Two parallel chords of length 8 cm and 6 cm of a circle of radius 5 cm are on the same side of centre then find the distance of one chord from another chord.
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Let the radius of the circle be r and let the distance of the longer chord from the center be x.
x^2 + 4^2 = r^2 …(1)
(x+1)^2 + 3^2 = r^2 …(2)
Equating (1) and (2)
x^2 + 4^2 = (x+1)^2 + 3^2 , or
x^2 + 16 = x^2 + 2x + 1 + 9, or
2x = 6 or x= 3.
From (1) r^2 = 3^2+ 4^2 = 5^2, so r = 5 cm.
x^2 + 4^2 = r^2 …(1)
(x+1)^2 + 3^2 = r^2 …(2)
Equating (1) and (2)
x^2 + 4^2 = (x+1)^2 + 3^2 , or
x^2 + 16 = x^2 + 2x + 1 + 9, or
2x = 6 or x= 3.
From (1) r^2 = 3^2+ 4^2 = 5^2, so r = 5 cm.
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