If the line $3x + 4y – 1 = 0$ touches the circle ${(x – 1)^2} + {(y – 2)^2} = {r^2}$, then the value of $r$ will be

The two tangents to a circle from an external point are always

Lines are drawn from a point $P (-1, 3)$ to a circle $x^2 + y^2 – 2x + 4y – 8 = 0$. Which meets the circle at $2$ points $A$ & $B$, then the minimum value of $PA + PB$ is

Statement $1$ : The only circle having radius $\sqrt {10} $ and a diameter along line $2x + y = 5$ is $x^2 + y^2 – 6x +2y = 0$.
Statement $2$ : $2x + y = 5$ is a normal to the circle $x^2 + y^2 -6x+2y = 0$.

The centres of two circles $C_1$ and $C_2$ each of unit radius are at a distance of $6$ units from each other. Let $P$ be the mid point of the line segment joining the centres of $C_1$ and $C_2$ and $C$ be a circle touching circles $C_1$ and $C_2$ externally. If a common tangent to $C_1$ and $C$ passing through $P$ is also a common tangent to $C_2$ and $C$, then the radius of the circle $C$ is