Question

Draw a different pair of circles. How many points does each pair have in common? What is the maximum number of common points?

Answer 1

Hint: To solve this question, we will draw all possible figures of pairs of circles. From there we will get the number of common points each pair will have in common. And we will also get the maximum number of common points two circles can have, by looking at the figures.

Complete step-by-step answer:
We have been given the idea that we need to draw different pairs of circles, there we need to check how many points each pair has in common. Then we need to find the maximum number of common points.
So, we will draw different pairs of circles.
\[1.\]In this figure, we have taken a pair of circles, where O is the centre of one circle and C is the centre of another circle. Both the circles are of the same radius, and are placed far from each other.
 

In this figure, number of common points $ = 0$

\[2.\]In this figure, we have taken a pair of circles, where O is the centre of one circle and C is the centre of another circle. Both the circles are of the same radius, and are close to each other.

In this figure, number of common points $ = 1$

\[3.\]In this figure, we have taken a pair of circles, where O is the centre of one circle and C is the centre of another circle. Both the circles are of the same radius, and are overlapping each other.
 

In this figure, number of common points $ = 2$
\[4.\]In this figure, we have taken a pair of circles, where O is the centre of one circle and C is the centre of another circle. Both the circles are of different radius.

In this figure, number of common points $ = 1$

\[5.\]In this figure, we have taken a pair of circles, where O is the centre of one circle and C is the centre of another circle. Both the circles are of different radius.

In this figure, number of common points $ = 1$
Thus, from the figure of different pair of circles, we get the maximum number of common points is \[2.\]

Note: While solving this question, students should recall all the possible pair of circles one can draw, because this step is very important, we can’t leave even one figure also, as if we leave even one diagram we won’t get the correct answer. As we are asked to get the maximum number of common points.