The equation of the incircle of the triangle formed by the lines $x=0, y=0$ and $3x+4y-24=0$ is

If $(a, b)$ is the centre of the circle passing through the vertices of the triangle formed by $x+y=6, 2x+y=4$ and $x+2y=5$,then $(a, b)$ is

The angle of intersection of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ and the circle $x^2 + y^2 = ab$ is

The radius of the circle passing through the points $(5,7)$,$(2,-2)$,and $(-2,0)$ is (in $units$)

If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b=$

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