The points $A, B, C, D, E$ are marked on the circumference of a circle in clockwise direction such that $\angle ABC = 130^{\circ}$ and $\angle CDE = 110^{\circ}$. The measure of $\angle ACE$ in degrees is: (in $^{\circ}$)

If $y=2x$ is a chord of the circle $x^2+y^2-10x=0$,then the equation of the circle with this chord as diameter is

Let $\alpha$ be an integer multiple of $8$. If $S$ is the set of all possible values of $\alpha$ such that the line $6 x + 8 y + \alpha = 0$ intersects the circle $x^2 + y^2 - 4 x - 6 y + 9 = 0$ at two distinct points,then the number of elements in $S$ is

Let $R$ be a rectangle,$C$ be a circle,and $T$ be a triangle in the plane. The maximum possible number of points common to the perimeters of $R, C$ and $T$ is

The equation of the circle inscribed in a square formed by the lines $x+y-2=0$,$x+y-6=0$,$x-y+1=0$ and $x-y+5=0$ is

If the points $(2, 0), (0, 1), (4, 5)$ and $(0, c)$ are concyclic,then $c$ is equal to