if two circles intersect at two points prove that their centres lie on the perpencular bisector of the common chord .
Answers
Hello mate =_=
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Solution:
Construction:
1) Draw two circles with centres O and O'.
2)Join A and B to get a common chord AB.
3) Join O and O' with the mid-point M of AB.
To prove: Centres lie on the perpendicular bisector of the common chord. In other words, we need to prove that OO' is a straight line and ∠AMO=∠AMO′=90°
In △AOB, M is the mid-point of chord AB.
⇒∠AMO=90° .....(1)
(The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.)
Similarly, in △AO′B, M is the mid-point of chord AB.
⇒∠AMO′=90° .......(2)
(The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.)
hope, this will help you.
Thank you______❤
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