Find the length of a chord which is at a distance of 3 cm from the center of a circle of radius 5 cm.


Let distance OC = 3 cm


Radius = OA = 5 cm


Draw OCAB


In triangle OCA,


OA2 = OC2 + AC2


⇒ 52 = 32 + AC2


⇒ AC2= 16


⇒ AC = 4 cm __________________ (i)


Now,


AB = 2 AC


⇒ AB = 8 cm [From equation (i)]


Hence, length of a chord = 8 cm.


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