In the given figure, a line intersects a circle at two points A and B. Now a point P, as shown in the figure, is fixed and the line is rotated about P in both directions until the points A and B coincide. How many times will they coincide?
In the given figure, a line intersects a circle at two points A and B. Now a point P, as shown in the figure, is fixed and the line is rotated about P in both directions until the points A and B coincide. How many times will they coincide?
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 point T as shown
When the line is rotated anticlockwise, the points A and B initially go further 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 figures above.
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 point T as shown
When the line is rotated anticlockwise, the points A and B initially go further 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 figures above.
