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Centre of two concentric circles is O. The area of two circles is 616 cm2 and 154 cm2 respectively. A tangent is drawn through point A on the larger circle to the smaller circle. This tangent touches small circle at B and intersects larger circle at C. What is the length (in cm) of AC?

Centre of two concentric circles is O. The area of two circles is 616 cm2 and 154 cm2 respectively. A tangent is drawn through point A on the larger circle to the smaller circle. This tangent touches small circle at B and intersects larger circle at C. What is the length (in cm) of AC? Correct Answer 14√3, 14√3

AC is a chord to the large circle

OB is the tangent to the small circle

∴ OB is perpendicular to AC

AC is bisected by OB

In triangle OAB

OA2 = OB2 + AB2

AB2 = OA2 - OB2 = R2 - r2

⇒ (π R2 - π r2)/π

⇒ (Area of larger circle - Area of smaller circle)/π

⇒ (616 - 154)/(22/7)

⇒ 462/(22/7) = 147

AB = √147 = 7√3

AC = 2 × AB = 14√3 cm

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