Dr. SK Goyal Solutions for Chapter: Circle, Exercise 12: FILL IN THE BLANKS

The radical centre of three circles described on the three sides of a triangle as diameter is_____

If $\left(2,5\right)$ is an interior point of the circle $x^2+y^2-8x-12y+p=0$ and the circle neither cuts nor touches any one of the axes of co-ordinates, then $p\in (......)$.

The circles ${\left(x-a\right)}^2+{\left(y-b\right)}^2=c^2$ and ${\left(x-b\right)}^2+{\left(y-a\right)}^2=c^2$ touch each other then $a=$

In the figure, $OABC$ is a square of side $6\mathrm{cm}$, then the equation of the smallest circle is _____

The equation of largest circle passing from $\left(1,1\right)$ and $\left(2,2\right)$ and always in first quadrant is _____

From a point $A\left(1,1\right)$ on the circle $x^2+y^2-4x-4y+6=0$, two equal chords $AB$ and $AC$ of length $2$ units are drawn. The equation of chord $BC$ is _____

The locus of a point which moves such that the sum  of its distances from three vertices of a triangle $ABC$ is constant is a circle whose centre is at the .

$\alpha ,\beta$ and $\gamma$ are parametric angles of three points $P,Q$ and $R$ respectively. On the circle $x^2+y^2=1,A$ is the point $\left(-1,0\right)$. If the lengths of the chords $AP,AQ$ and $AR$ are in $GP$, then $\cos \alpha /2,\cos \beta /2$, and $\cos \gamma /2$ are in _____