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Let A 1 be a circle of radius r1. An equilateral triangle B1 is inscribed in this circle A1 such that all the vertices of B1 lie on the circumference of A1. Another circle A2 is inscribed in the triangle By such that touches all three sides of B1. Another equilateral triangle B^ is inscribed in the circle A2. Another circle A3 is inscribed in the triangle B2 and so on. What is the ratio of the perimeter of A16  to the perimeter of B13 ?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let A 1 be a circle of radius r1. An equilateral triangle B1 is inscri...
Radius of circle A 1 is r1
It can be observed from the figure that, radius of A2 is rl2 and length of side of B1 is V3r1
Thus, the radii of circles A1, A2, A3 and so on, form a GP with common ratio 1/2.
Also, the length of each side of triangles B, B2, #3 and so on, form a GP with common ratio 1/2.
The ratio of the perimeter of A16 to the perimeter of 513


Hence, option 1.
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Let A 1 be a circle of radius r1. An equilateral triangle B1 is inscribed in this circle A1 such that all the vertices of B1 lie on the circumference of A1. Another circle A2 is inscribed in the triangle By such that touches all three sides of B1. Another equilateral triangle B^ is inscribed in the circle A2. Another circle A3 is inscribed in the triangle B2 and so on. What is the ratio of the perimeter of A16to the perimeter of B13?a)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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