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A chord of a circle of radius 10 em subtends a right angle at its centre. The length of the chord (in em) is - Mathematics

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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`

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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

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
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