1
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Question

# In the given figure, a line intersects a circle at points A and B. The line is rotated about the point P in both the directions until the points A and B coincide. How many times will they coincide?

A

1

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B

2

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C

0

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D

Infinitely many times

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Solution

## The correct option is B 2 When the line is rotated clockwise about P, as shown in the figure below, the points A and B get closer to each other until they coincide at the point T. When the line is rotated anticlockwise as shown below, the points A and B initially move away from each other until they become the ends of a diameter (denoted by A’ and B’), in which case the line would pass through the centre of the circle (denoted by O). Then, the points A and B would come closer to each other until they coincide at point S. Hence, there are two places where the points A and B would coincide, and those are points S and T as shown in the above figures.

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