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Question
Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is ______.
Options
12 cm
13 cm
14 cm
15 cm
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Solution
Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is 13 cm.
Explanation:
Let the chord be AB = 24 cm
Distance of the chord from the centre O is 5 cm.
AO is the radius of the circle.
Perpendicular from the centre of the circle to the chord bisects the chord.
So, AC = CB
In ΔAOC,
OC2 + AC2 = AO2
⇒ 52 + 122 = AO2
⇒ AO2 = 25 + 144
⇒ AO2 = 169
⇒ AO = 13 cm
Thus, the radius of the circle is 13 cm.
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