Q7 of 45 Page 12

Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger circle of length 48 cm, touches the smaller circle. Find the value or r. (CBSE 2011)


The angle between tangent and radius is 90°.
∴ ∠ OCA=90°


Also ∠OCB=90°


⇒ OC ⊥ AB


AC=1/2 AB(Perpendicular from center bisects chord(AB) of the circle)


∴ AC= 1/2 (48)=24cm


Now we consider the right-angled triangle OAC,


(OA)2=(OC)2 + (AC)2


(r)2=(7)2 + (24)2 =625


r=√ 625 =25cm

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