The circle $x^2+y^2-6x-10y+p=0$ neither intersects nor touches the coordinate axes and the point $(1,4)$ lies inside the circle. Then the range of possible values of $p$ is

Let $A(2,3)$,$B(3,-1)$,and $C(-3,2)$ be three points. If the centre of the circle passing through $A$,$B$,and $C$ is $O(h, k)$,then find the value of $2k - 4h$.

Tangent $L_1 \equiv 3x - 4y - 8 = 0$ and the chord $L_2 \equiv x + y - 1 = 0$ are at a distance of $2$ and $\sqrt{2}$ units respectively from the centre of a circle $S$. $(h, k)$ is the centre of $S$ such that $h^2 + k^2 = 13$. If the midpoint of the chord $L_2 = 0$ is $(\alpha, \beta)$ and the radius of the circle is $r$,then $\alpha + \beta + r =$

The angle subtended by the chord $x+y-1=0$ of the circle $x^2+y^2=1$ at the origin is

The radius of the circle having three chords along the $y$-axis,the line $y=x$,and the line $2x+3y=10$ is

Given $r_1, r_2 > 0$ and $C_1, C_2$ are the centres of two circles having only two common tangents. If $C_1 C_2 = r_1 + r_2$,which of the following is correct?