The least distance of the point $(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ is

Let $XY$ be the diameter of a semi-circle with center $O$. Let $A$ be a variable point on the semi-circle and $B$ another point on the semi-circle such that $AB$ is parallel to $XY$. The value of $\angle BOY$ for which the inradius of $\triangle AOB$ is maximum,is

Two circles with equal radii intersect at the points $(0, 1)$ and $(0, -1).$ The tangent at the point $(0, 1)$ to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is

The angle between the circles $x^2+y^2-4x-6y-3=0$ and $x^2+y^2+8x-4y+11=0$ is

The centre of the smallest circle touching the circles $x^2 + y^2 - 2y - 3 = 0$ and $x^2 + y^2 - 8x - 18y + 93 = 0$ is:

Three circles of radii $1, 2$ and $3$ units respectively touch each other externally in the plane. The circumradius of the triangle formed by joining the centers of the circles is