The least and the greatest distances of the point $(10, 7)$ from the circle $x^{2} + y^{2} - 4x - 2y - 20 = 0$ are

Let $C$ be a circle having centre in the first quadrant and touching the $x$-axis at a distance of $3$ units from the origin. If the circle $C$ has an intercept of length $6\sqrt{3}$ on the $y$-axis, then the length of the chord of the circle on the line $x - y = 3$ is:

If $(m_i, \frac{1}{m_i}), i = 1, 2, 3, 4$ are concyclic points,then the value of $m_1 \cdot m_2 \cdot m_3 \cdot m_4$ is

If the radical axis of the circles $x^2 + y^2 - 1 = 0$ and $x^2 + y^2 - 2x - 2y + 1 = 0$ forms a triangle of area $A$ with the coordinate axes,then the value of $\frac{1}{A}$ is

The circumference of a circle passing through the point $(4,6)$ with two normals represented by $2x - 3y + 4 = 0$ and $x + y - 3 = 0$ is (in $\pi$)

$A$ square is inscribed in the circle $x^2+y^2-2x+4y-93=0$ with its sides parallel to the coordinate axes. Which of the following can be one of the vertices of the square?