In a circle of diameter $40 \, cm$,the length of a chord is $20 \, cm$. Find the length of the minor arc of the chord.

If the line $y = mx + 1$ meets the circle $x^2 + y^2 + 3x = 0$ at two points equidistant from the $y$-axis and on opposite sides,then:

If the circle $x^2 + y^2 - 6x - 8y + (25 - a^2) = 0$ touches the $x$-axis,then $a$ equals

Let $C$ be a circle passing through the points $A (2,-1)$ and $B (3,4)$. The line segment $AB$ is not a diameter of $C$. If $r$ is the radius of $C$ and its centre lies on the circle $(x-5)^{2}+(y-1)^{2}=\frac{13}{2}$,then $r^{2}$ is equal to

On the circle with center $O$,points $A$ and $B$ are such that $OA = AB$. $A$ point $C$ is located on the tangent at $B$ to the circle such that $A$ and $C$ are on the opposite sides of the line $OB$ and $AB = BC$. The line segment $AC$ intersects the circle again at $F$. Then,the ratio $\angle BOF : \angle BOC$ is equal to

If a circle with centre at $(-1, 1)$ touches the line $x + 2y + 4 = 0$,then the coordinates of the point of contact are: