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Question
Chords AB & CD of a circle are parallel to each other and lie on opposite sides of the centre of the circle. If AB = 36 cm, CD = 48 cm and the distance between the chords is 42 cm. Find the radius of the circle.
Chords AB & CD of a circle are parallel to each other and lie on opposite sides of the centre of the circle. If AB = 36 cm, CD = 48 cm and the distance between the chords is 42 cm. Find the radius of the circle.
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Solution
In ΔEOB, r2 = (42−x)2+ (18)2 ------ (i)
In ΔFOD, r2 = (24)2 +x2 ------ (ii)
Subtract (i) from (ii), we get
(42−x)2+(18)2=(24)2+ x2
(42−x)2−x2=(24)2−(18)2
(42- 2x)(42) = 6×(42)
x = 18 cm
Putting the value of x in equation (ii), we get
r2=(18)2+(24)2
r = 30 cm
In ΔEOB, r2 = (42−x)2+ (18)2 ------ (i)
In ΔFOD, r2 = (24)2 +x2 ------ (ii)
Subtract (i) from (ii), we get
(42−x)2+(18)2=(24)2+ x2
(42−x)2−x2=(24)2−(18)2
(42- 2x)(42) = 6×(42)
x = 18 cm
Putting the value of x in equation (ii), we get
r2=(18)2+(24)2
r = 30 cm
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