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Question
A chord of a circle of radius 10 em subtends a right angle at its centre. The length of the chord (in em) is
`(A) 5sqrt 2`
`(B) 10 sqrt2`
`(C)5/sqrt2`
`(D) 10sqrt 3`
Solution
Correct answer: B
Given ∠ AOB is given as 90º
ΔAOB is an isosceles triangle since OA = OB
Therefore ∠OAB = ∠OBA = 45º
Thus ∠ AOP = 45º and ∠ BOP = 45º
Hence ΔAOP and ΔBOP also are isosceles triangles
AP = OP and OP PB
In ΔAOP
x2 + x2 = 102 [Pythagoras theorem]
Thus 2 x2 = 100
x=5√2
Hence length of chord AB = 2 x = 5√2+5√2=10√2
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