Q5 of 105 Page 598

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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