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The centre of two concentric circles is O. The areas of the two circles are 616 cm2 and 154 cm2, respectively. A tangent is drawn through point A on the larger circle to the smaller circle. This tangent touches the smaller circle at B and intersects the larger circle at C. What is the length (in cm) of AC?
  • a)
    12√3
  • b)
    14√3
  • c)
    10√6
  • d)
    18√2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The centre of two concentric circles is O. The areas of the two circl...
Let the radius of bigger circle be R cm and radius of smaller circle be r cm
Area of the larger circle = 616 cm2
πR2 = 616
r = 14 cm
Area of the smaller circle = 154 cm2
πr2 = 154
r = 7 cm
In triangle OBA, using Pythagoras theorem
OA2 = OB2 + AB2
142 = 72 + AB2
196 - 49 = AB2
Now, AC = 2AB
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The centre of two concentric circles is O. The areas of the two circles are 616 cm2 and 154 cm2, respectively. A tangent is drawn through point A on the larger circle to the smaller circle. This tangent touches the smaller circle at B and intersects the larger circle at C. What is the length (in cm) of AC?a)12√3b)14√3c)10√6d)18√2Correct answer is option 'B'. Can you explain this answer?
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