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if two circles intersect at two points,prove that their centres lie on the perpendicular bisector of the common chord.
Asked by mehtarakhi3 | 09 Feb, 2019, 03:33: PM
Figure shows two circles intersect at A and B, AB is common chord. P and Q are centres of circles.

Let C is mid point of AB. let us join PC and QC.

In a circle, line drawn from centre of circle to the mid point of chord is perpendicular to that chord.
hence PC is perpendicular to AB and QC is perpendicular to AB.

Since PCA and ACQ are right angles and C is midpoint of AB, PQ is perpendicular bisector of AB.
Hence the centres of circle P and Q lie in the perpendicular bisector of common chord AB of two intersecting circles at A and B
Answered by Thiyagarajan K | 10 Feb, 2019, 12:31: PM

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