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Question
Radius of a circle is 34 cm and the distance of the chord from the centre is 30 cm, find the length of the chord.
Solution
Let O be the center of the circle and seg AB is its chord.
seg OC ⊥ chord AB such that, A-C-B
OA = 34 cm
OC = 30 cm
In ∆OCA, From Pythagoras theorem,
OA2 = OC2 + AC2
∴ 342 = 302 + AC2
∴ 1156 = 900 + AC2
∴ AC2 = 1156 – 900
∴ AC2 = 256
∴ AC = `sqrt(256)`
∴ AC = 16 cm
∴ AC = `1/2` AB ...(The perpendicular drawn from the center of the circle to the chord bisects the chord.)
∴ 16 = `1/2` AB
∴ AB = `16 xx 2`
∴ AB = 32 cm
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