If the locus of the mid-point of the chords of the circle $x^2+y^2=25$, which subtend a right angle at the origin is given by $\frac{x^2}{\alpha^2}+\frac{y^2}{\alpha^2}=1$, then $|\alpha|=$

The radical centre of the circles $x^2+y^2+2 x+3 y+1=0$, $x^2+y^2+x-y+3=0, x^2+y^2-3 x+2 y+5=0$

If a circle is inscribed in an equilateral triangle of side $a$, then the area of any square (in sq units) inscribed in this circle is

If the line segment joining the points $(1,0)$ and $(0,1)$ subtends an angle of $45^{\circ}$ at a variable point $P$, then the equation of the locus of $P$ is