The radius of the circle having $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ as its tangents 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 $x^2+y^2=25$,then $\log _5[\max (3 x+4 y)]$ is

$A$ circular wire of radius $7\,cm$ is cut and bent again into an arc of a circle of radius $12\,cm$. The angle subtended by the arc at the centre is ......$^o$

$A$ cow is tied to a post by a rope. The cow moves along a circular path,always keeping the rope tight. If it describes an arc of $44 \ m$ when it has traced out $72^{\circ}$ at the centre,the length of the rope is: (in $m$)

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