How many circles can be drawn each touching all the three lines x+y=1, x+1=y, 7x-y=6

Equation of the circle passing through A(1, 2), B(5, 2) so that the angle substended by AB at points on the circle is π/4 is

Match the following

The number of points where the circle x²+y²-4x-4y=1 cuts the sides of the rectangle x=2 , x=5 , y=-1 and y=5 is

If 5x-12y+10=0 and 12y-5x+16=0 are two tangents to a circle,then the radius of the circle is

The tangents at (3, 4), (4, -3) to the circle x²+y²=25 are

The equation of the circle cutting orthogonally circles x²+y²+2x+8=0, x²+y²-8x+8=0 and which touches the line x-y+4=0 is

If the circle S=x²+y²-16=0 intersects another circle S’=0 of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to 3/4 then the centre of S’=0 is

The locus of the midpoints of chords of the circle x²+y²=25 which touch the circle (x-2)²+(y-5)²=289 is

If (3,2 )is limiting point of the coaxal system of circles whose common radical axis is 4x+2y=11, then the other limiting point is