C1:x^2+y^2=25 , C2:x^2+y^2-2x-4y-7=0 be two circles intersecting each ither at A and B. What is the point of intersection of tangents of C1 at A and B?

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Please find below the solution to the asked query:

We haveC1:x2+y2-25=0C2:x2+y2-2x-4y-7=0Equation of common chord AB isC1-C2=0x2+y2-25-x2+y2-2x-4y-7=0x2+y2-25-x2-y2+2x+4y+7=02x+4y-18=0x+2y-9=0...iNow tangents are made at A and B. If tangents meet at Px1,y1, thenAB is chord of contact with respect to Pequation of chord of contact isT=0xx1+yy1-25=0...iiCompare with i and iix11=y12=-25-9x1=259y1=509x1,y1=259,509

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