What is the distance between two parallel chords which are drawn at the ends of the diameter of a circle whose radius is 10 cm ?
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Answers
Step-by-step explanation:
Radius of the circle, with centre at O = 24 cm.
Length of chord AB = 12 cm. Mid point is E.
Length of chord CD = 15 cm. Mid point is F.
Case 1. When AB and CD are on the same side of O.
OE = [24^2 - 6^2]^0.5 = [30*18}^0.5 = 23.24 cm.
OF = [24^2 - 7.5^2]^0.5 = [31.5*16.5}^0.5 = 22.80 cm.
The distance between the chords Ab and CD = 23.24–22.80 = 0.44 cm
Case 1. When AB and CD are on the opposite sides of O.
OE = [24^2 - 6^2]^0.5 = [30*18}^0.5 = 23.24 cm.
OF = [24^2 - 7.5^2]^0.5 = [31.5*16.5}^0.5 = 22.80 cm.
The distance between the chords AB and CD = 23.24+22.80 = 46.04 cm
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Step-by-step explanation:
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Two parallel chords are drawn in a circle of diameter 30 cm.The length if one chord is 24 cm and the distance between the two chords is 21 cm find the length of the other chord.
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ANSWER
AD=Diameter=30 cm
CD=Chord=24 cm
x+y=21
Again, y
2
+12
2
=15
2
⇒y
2
=15
2
−12
2
⇒y
2
=81
⇒y=9
x=21−9=12
Now, 12
2
+a
2
=16
2
a
2
=16
2
−12
2
=81
⇒a=9
Length of the chord AB=2×9=18cm
solution