JEE Advance - Mathematics (1993 - No. 19)

Consider a family of circles passing through two fixed points A (3, 7) and B (6, 5). Show that the chords on which the circle $${x^2}\, + \,{y^2} - \,4x - \,6y - 3 = 0$$ cuts the members of the family are concurrent at a point. Find the coordinate of this point.
(1, 1)
(2, 23/3)
(3, 7)
(6, 5)
(4, 6)

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