$P$ and $Q$ are the points of trisection of the line segment joining the points $(3,-7)$ and $(-5,3)$. If $P Q$ subtends right angle at a variable point $R$, then the locus of $R$ is

If $A(1,2), B(2,1)$ are two vertices of an acute angled triangle and $S(0,0)$ is its circumcenter, then the angle subtended by $A B$ at the third vertex is

A circle passing through the points $(1,1)$ and $(2,0)$ touches the line $3 x-y-1=0$. If the equation of this circle is $x^{2}+y^{2}+2 g x+2 f y+c=0$, then a possible value of $g$ is

A circle passes through the points $(2,0)$ and $(1,2)$. If the power of the point $(0,2)$ with respect to this circle is 4 , then the radius of the circle is