Centre of two concentric circles is O. The areas 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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 14√3
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Application |
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The areas of two circles is 616 cm2 and 154 cm2 respectively. Radius of two circles are AO and OB. So, 22/7 × (AO)2 = 616 AO = 14 cm And 22/7 × (BO)2 = 154 BO = 7 cm Triangle ABO is a right angle triangle (Since AB is the tangent to the circle); ∴ (AO)2 = AB2 + OB2 ⇒ AB2 = 142 – 72 ⇒ AB2 = 147 ∴ AB = 7√3 cm And AC = 2AB = 14√3 cm |
