The coordinates of the middle point of the chord intercepted on line lx+my+n=0 by the circle  x2+y2=a2 are

Let x1,y1  e the mid-point of the chord  intercepted by the circle  x2+y2=a2 on the line  lx+my+n=0Then, the equation of the chord of the circle  x2+y2=u2whose middle point is  x1,y1 is xx1+yy1−a2=x12+y12−a2⇒ xx1+yy1=x12+y12                    ........(i)Clearly,  lx+my+n=0 and (i)    represents the same line. ∴ x1l=y1m=−x12+y12n=λ, say ⇒ x1=lλ,y1=mλ and x12+y12=−nλ⇒ l2+m2λ2=−nλ⇒ λ=−nl2+m2∴ x1=−lil2+m2,y1=−mml2+m2Hence, t e reqmre point  is  −ml2+m2,−mn12+m2