Home
Class 9
MATHS
If two circles intersect in two points, ...

If two circles intersect in two points, prove that the line through the centres is the perpendicular bisector of the common chord.

Text Solution

Verified by Experts

`AB` is the chord of the circle centered at `O` and it is also the chord of the circle centered at `O’`.
Let `OO'` intersect `AB` at `M`.
In `/_\OAO'` and `/_\OBO'`, we have
`OA = OB` (radii of same circle)
`O'A = O'B` (radii of same circle)
`OO' = OO'` (common)
Triangle `OAO'` and `OBO'` are congruent by side side side congruency.
`/_AOO' =/_BOO'`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Two circles of radii 5\ c m\ a n d\ 3c m intersect at two points and the distance between their centres is 4c m . Find the length of the common chord.

Two circles of radii 5\ c m\ a n d\ 3c m intersect at two points and the distance between their centres is 4c mdot Find the length of the common chord.

Two circles of radil 5c m and 3c m intersect at two points and the distance between their centres is 4c mdot Find the length of the common chord.

If a number of circles pass through the end points P and Q of a line segment PQ, then prove their centres lie on the perpendicular bisector of PQ.

If two equal chords of a circle intersect within the circle, prove that: the segments of the chord are equal to the corresponding segments of the other chord.

If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

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.

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.

If a number of circles pass through the end points P and Q of a line segment PQ, then Prove that their centres lie on the perpendicular bisector of PQ.

Two circles of radii 10 cm and 17 cm . Intersecting each other at two points and the distances between their centres is 21 cm . Find the length of the common chords.