Question:
In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is
- \(\sqrt {12} \)
- \(\sqrt {14} \)
- \(\sqrt {13} \)
- \(\sqrt {11} \)
Correct Answer: 3
Let the 6 cm long chord be x cm away from the centre of the circle. Let the radius of the circle be r cm.
The perpendiculars from the centre of the circle to the chords bisect the chords.
$r^{2}=x^{2}+3^{2}=(x+1)^{2}+2^{2}$
Solving, $x=2$ and $r=\sqrt{13}$
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