# Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

**Solution:**

The perpendicular bisector of the common chord passes through the centers of both circles.

Given that the circles intersect at two points, so we can draw the above figure. Let AB be the common chord. Let O and O’ be the centers of the circles, respectively.

O’A = 5 cm, OA = 3 cm

OO’ = 4 cm [Given distance between the centres is 4cm]

Since the radius of the bigger circle is more than the distance between the 2 centers, we can say that the center of the smaller circle lies inside, the bigger circle itself.

OO’ is the perpendicular bisector of AB.

So, OA = OB = 3 cm

AB = 3 cm + 3 cm = 6 cm [Since, O is the mid point of AB]

The length of the common chord is 6 cm.

It is also evident that the common chord is the diameter of the smaller circle.

**Video Solution:**

## 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.

### Maths NCERT Solutions Class 9 - Chapter 10 Exercise 10.4 Question 1:

**Summary:**

If two circles of radii 5cm and 3cm intersect at two points and the distance between their centers is 4cm, then the length of the common chord is 6cm.