The chord of a circle of radius 10 cm subtends a right angle at its center. The length of the chord (in cm) is
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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