Q. The circle cuts the circles and orthogonally. If the common chord of and is , then the centre of

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Solution:

Let the equation of circle is



matheal is orthogonally to and
(i)
(ii)
From Eqs. (i) and (ii),
(iii)
Common chord of and
=.(iv)
Given common chord is

Eqs. (iv) and (v) are coincide

(vi)
Solving Eqs. (iii) and (vi), we get

Centre of circle,