Question : In a circle of radius 5 m, AB and CD are two equal and parallel chords of length 8 m each. What is the distance between the chords?
Option 1: 5 m
Option 2: 6 m
Option 3: 3 m
Option 4: 8 m
Correct Answer: 6 m
Solution : Given: Radius($OB$) = 5 m Chord ($AB$) = 8 m So, $AQ = BQ = \frac{8}{2} = 4$ m By Pythagoras' theorem, $OQ^2=OB^2-BQ^2$ ⇒ $OQ^2=5^2-4^2$ ⇒ $OQ^2=25-16$ ⇒ $OQ^2=9$ ⇒ $OQ=3$ $\therefore$ Distance between the chord $PQ=2\times 3 = 6$ m Hence, the correct answer is 6 m.
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Question : Chords AB and CD of a circle intersect externally at P. If AB = 6 cm, CD = 3 cm, and PD = 5 cm, then the length of PB is:
Option 1: 5 cm
Option 2: 7.35 cm
Option 3: 6 cm
Option 4: 4 cm
Question : Two parallel chords of lengths 40 cm and 48 cm are drawn in a circle of radius 25 cm. What will be the distance between the two chords?
Option 1: 8 cm
Option 2: 15 cm
Option 3: 22 cm
Option 4: Either 8 cm or 22 cm
Question : In a circle, chords AB and CD intersect internally at E. If CD = 18 cm, DE = 5 cm, AE = 13 cm, then the length of BE is:
Option 1: 4 cm
Option 2: 7 cm
Option 3: 3 cm
Option 4: 5 cm
Question : PQ and RS are two parallel chords of a circle such that PQ is 48 cm and RS is 40 cm. If the chords are on the opposite sides of the centre and the distance between them is 22 cm, what is the radius (in cm) of the circle?
Option 1: 25
Option 2: 24
Option 3: 35
Option 4: 22
Question : A line touches a circle of radius 6 cm. Another line is drawn which is tangent to the circle. If the two lines are parallel, then the distance between them is:
Option 2: 12 cm
Option 3: 10 cm
Option 4: 6 cm
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