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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