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Question
AB, CD are parallel chords of a circle 7 cm apart. If AB = 6 cm, CD = 8 cm, find the radius of the circle.
Solution
Let O be the centre of the circle OM and ON are perpendiculars on AB and CD.
MON is one straight line.
Here
AM = `1/2`AB = 3 cm
CN = `1/2`CD = 4 cm
Let, ON = x cm and radius OA = OC = r cm
From right angled triangle OCN,
ON2 = OC2 - CN2 ...(By Pythagoras Theorem)
x2 = r2 - 16 ...(1)
From right-angled triangle OAM,
OM2 = OA2 - AM2 ...(By Pythagoras Theorem)
(7 - x)2 = r2 - 9 ...(2)
From (1) and (2),
(7 - x)2 - x2 = 7
49 + x2 - 14x - x2 = 7
14x = 42
x = 3
r2 = x2 + 16 ....(From(1))
r2 = 9 + 16 = 25
r = 5 cm
Hence, the radius of the circle is 5 cm.
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