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Quantitative Aptitude

Mixture & Alligations

Let C be a ci...

Question

Let C be a circle with centre $P_{0}$ and AB be a diameter of C. Suppose $P_{1}$ is the mid point of the line segment $P_{0} B, P_{2}$ is the mid-point of the line segment $P_{1} B$ and so on. Let $C_{1}, C_{2}, C_{3}$ ,… be circles with diameters $P_{0} P_{1}, P_{1} P_{2}, P_{2} P_{3}$ … respectively. Suppose the circles $C_{1}, C_{2}, C_{3}$ … are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is :

A

8 : 9

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B

9 : 10

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C

10 : 11

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D

11 : 12

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Solution

The correct option is D 11 : 12
Option (D) is the correct answer. Check the video for the approach.

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Let $c_{1} : x^{2} + y^{2} = 1; C_{2} : (x - 10)^{2} + y^{2} = 1 a n d C_{3}; x^{2} + y^{2} - 10 x - 42 y + 457 = 0$ be three circle.A circle C has been drawn to touch circles $C_{1}$ and $C_{2}$ externally and $C_{3}$ internally. Now circles $C_{1}, C_{2}$ and $C_{3}$ start rolling on the circumference of circle C in anticlockwise direction with constant speed. The centroid of the triangle formed by joining the centres of rolling circles $C_{1}, C_{2}$ and $C_{3}$ lies on

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