Q. 55.0( 1 Vote )

# The chord of a circle of radius 10 cm subtends a right angle at its center. The length of the chord (in cm) isA. B. C. D.

Let us consider a circle with center O and AB be any chord that subtends 90° angle at its center.

Now, In OAB

OA = OB = 10 cm

And as AOB = 90° ,

By Pythagoras Theorem,

[i.e. (Hypotenuse)2 = (Base)2 + (Perpendicular)2]

(OA)2 + (OB)2 = (AB)2

(10)2+ (10)2 = (AB)2

100 + 100 = (AB)2

AB = √200 = 10√2

So, Correct option is C .

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