If the length of the chord of the circle $x^{2}+y^{2}=r^{2}$ $(r>0)$ along the line $y-2x=3$ is $r$,then $r^{2}$ is equal to

The acute angle between the curves $x^2+y^2=x+y$ and $x^2+y^2=2y$ is

If one end of the diameter of the circle $x^2+y^2-4x-6y+11=0$ is $(3,4)$,then the other end of the diameter is

Let $AB$ be a line segment with mid-point $C$ and $D$ be the mid-point of $AC$. Let $C_1$ be the circle with diameter $AB$ and $C_2$ be the circle with diameter $AC$. Let $E$ be a point on $C_1$ such that $EC$ is perpendicular to $AB$. Let $F$ be a point on $C_2$ such that $DF$ is perpendicular to $AB$ and $E$ and $F$ lie on opposite sides of $AB$. Then,the value of $\sin \angle FEC$ is

Let $ABCD$ be a square of side length $1$,and $\Gamma$ be a circle passing through $B$ and $C$,and touching $AD$. The radius of $\Gamma$ is

If a circle of radius $r$ touches the positive coordinate axes and also the circle $x^2+y^2-12x-10y+52=0$ externally,then the distance between the centres of the two circles is