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Let A1 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 B1 such that A2 touches all three sides of B1. Another equilateral triangle B2 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 o f A16 to the perimeter of B13 ?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let A1be a circle of radius r1. An equilateral triangle B1is inscribed...
Radius of circle A1 is r1
It can be observed from the figure that, radius of A2 is r1/2 and length of side of B1 is √3r1
Thus, the radii of circles A1, A2, Aand so on, form a GP with common ratio 1/2.
Also, the length o f each side o f triangles B1, B2 , B3 and so on, form a GP with common ratio 1/2.
Hence, option 1.
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Let A1be a circle of radius r1. An equilateral triangle B1is inscribed in this circle A1such that all the vertices of B1 lie on the circumference of A1. Another circle A2 is inscribed in the triangle B1such that A2 touches all three sides of B1. Another equilateral triangle B2 is inscribed in the circle A2.Another circle A3is inscribed in the triangle B2 and so on. What is the ratio of the perimeter o f A16to the perimeter of B13?a)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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Let A1be a circle of radius r1. An equilateral triangle B1is inscribed in this circle A1such that all the vertices of B1 lie on the circumference of A1. Another circle A2 is inscribed in the triangle B1such that A2 touches all three sides of B1. Another equilateral triangle B2 is inscribed in the circle A2.Another circle A3is inscribed in the triangle B2 and so on. What is the ratio of the perimeter o f A16to the perimeter of B13?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let A1be a circle of radius r1. An equilateral triangle B1is inscribed in this circle A1such that all the vertices of B1 lie on the circumference of A1. Another circle A2 is inscribed in the triangle B1such that A2 touches all three sides of B1. Another equilateral triangle B2 is inscribed in the circle A2.Another circle A3is inscribed in the triangle B2 and so on. What is the ratio of the perimeter o f A16to the perimeter of B13?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A1be a circle of radius r1. An equilateral triangle B1is inscribed in this circle A1such that all the vertices of B1 lie on the circumference of A1. Another circle A2 is inscribed in the triangle B1such that A2 touches all three sides of B1. Another equilateral triangle B2 is inscribed in the circle A2.Another circle A3is inscribed in the triangle B2 and so on. What is the ratio of the perimeter o f A16to the perimeter of B13?a)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
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