# Ex.10.3 Q3 Circles Solution - NCERT Maths Class 9

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## Question

If two circles intersect at two points, prove that their centers lie on the perpendicular bisector of the common chord.

Video Solution
Circles
Ex 10.3 | Question 3

## Text Solution

What is known?

Two circles intersecting at two points.

What is unknown?

To check whether their centers lie on the perpendicular bisector of the common chord.

Reasoning:

By theorem $$10.4$$, it is known that perpendicular bisector of a chord passes through its centre. Since the chord is common to both the circles, the centre should lie on the perpendicular bisector of the chord.

Steps:

Let the two circles intersect at point $${A}$$ and $${B}$$. Join $${AB}$$. $${AB}$$ is the common chord. By theorem $${10.4,}$$ it is known that perpendicular bisector of a chord passes through its centre.

As the chord $$AB$$ is common to both circles, the perpendicular bisector of the common chord should pass through their centers. So centre lies on the perpendicular bisector of the common chords.

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