A triangle is inscribed in a circle of radius 1. The distance between the orthocentre and the circumcentre of the triangle cannot be

If a circle passes through the points where the lines $3kx-2y-1=0$ and $4x-3y+2=0$ meet the coordinate axes then $k=$

All chords of the curve $x^2+y6\left(2\right)-10x-4y+4=0$, which make a right angle at $\left(8,-2\right)$ pass through

A circle passing through the point $\left(2,2\left(\sqrt{2}-1\right)\right)$ touches the pair of lines $x^2-y^2-4x+4=0$. The centre of the circle is

Equation of circle symmetric to the circle $x^2+y^2+16x-24y+183=0$ about the line $4x+7y+13=0$ is

If a chord of a the circle $x^2+y^2=32$ makes equal intercepts of length of l on the co-ordinate axes, then

Equation of circle inscribed in $\left|x-a\right|+\left|y-b\right|=1$ is

Let $A\left(-4,0\right)$ and $B\left(4,0\right)$. Then the number of points $C=\left(x,y\right)$ on the circle $x^2+y^2=16$ lying in first quadrant such that the area of the triangle whose vertices are A,B and C is a integer is

Let $A\left(1,2\right),B\left(3,4\right)$ be two points and $C\left(x,y\right)$ be a point such that area of $\Delta ABC$ is 3 sq. units and $\left(x-1\right)\left(x-3\right)+\left(y-2\right)\left(y-4\right)=0$. Then number of positions of C, in the xy plane is

P and Q are any two points on the circle $x^2+y^2=4$ such that PQ is a diameter. If $\alpha$ and $\beta$ are the lengths of perpendicular from P and Q on $x+y=1$ then the maximum value of $\alpha \beta$ is