ABCD is a square of side length 2 units. $${C_1}$$ is the circle touching all the sides of the square ABCD and $${C_2}$$ is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.

If P is any point of $${C_1}$$ and Q is another point on $${C_2}$$, then

$${{P{A^2}\, + \,P{B^2}\, + P{C^2}\, + P{D^2}} \over {Q{A^2} + \,Q{B^2}\, + Q{C^2}\, + Q{D^2}}}$$ is equal to

A circle is given by $${x^2}\, + \,{(y\, - \,1\,)^2}\, = \,1$$, another circle C touches it externally and also the x-axis, then thelocus of its centre is

If one of the diameters of the circle $${x^2} + {y^2} - 2x - 6y + 6 = 0$$ is a chord to the circle with centre (2, 1), then the radius of the circle is

The centre of circle inscibed in square formed by the lines $${x^2} - 8x + 12 = 0\,\,and\,{y^2} - 14y + 45 = 0$$, is