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

**Solution:**

In this, there are no common points.

In this, there is only one common point.

In this, there are two common points.

In a situation where two congruent circles are superimposed on each other, it can be understood as if we are drawing the same circle two times.

It is therefore concluded, there can be a maximum of two common points for different pairs of circles.

**ā Check: **NCERT Solutions Class 9 Maths Chapter 10

**Video Solution:**

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

Maths NCERT Solutions Class 9 Chapter 10 Exercise 10.3 Question 1

**Summary:**

If different pairs of circles are drawn, then there can be a maximum of two common points for different pairs of circles.

**ā Related Questions:**

- Suppose you are given a circle. Give a construction to find its center.
- If two circles intersect at two points, prove that their centers lie on the perpendicular bisector of the common chord.
- Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centers is 4 cm. Find the length of the common chord.
- If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

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