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Question
Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is ______.
Options
16 cm
8 cm
12 cm
32 cm
Solution
Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is 16 cm.
Explanation:
Let the chord be AB.
O be the centre and OC be the perpendicular drawn from the centre of the circle to the chord AB.
Perpendicular drawn from the centre of the circle to the chord bisects the chord.
AC = CB
OA is the radius = 10 cm
In ΔOAC,
OC2 + AC2 = OA2
⇒ 62 + AC2 = 102
⇒ 36 + AC2 = 100
⇒ AC2 = 64
⇒ AC = 8 cm
AC = CB = 8 cm
AB = AC + CB
= 8 + 8
= 16 cm
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