G Tewani Solutions for Chapter: Circles, Exercise 3: DPP

For all values of $m\in R$, the line $y-mx+m-1=0$ cuts the circle $x^2+y^2-2x-2y+1=0$ at an angle

If the line $\left|y\right|=x-\alpha , \alpha >0$ does not meet the circle $x^2+y^2-10x+21=0$, then $\alpha \in$

Let $C$ be the circle of unit radius centred at the origin. If two positive numbers $x_1$ and $x_2$ are such that the line passing through $\left(x_1, -1\right)$ and $\left(x_2, 1\right)$ is tangent to $C$, then

A circle of radius $5$ is tangent to the line $4x-3y=18$ at $M\left(3,-2\right)$ and lies above the line. The equation of the circle is

The line $y=mx$ intersects the circle $x^2+y^2-2x-2y=0$ and $x^2+y^2+6x-8y=0$ at points $A$ and $B$ (points being other than origin). The range of $m$ such that origin divides $AB$ internally is

If $C_1: x^2+y^2={\left(3+2\sqrt{2}\right)}^2$ be a circle. $PA$ and $PB$ are pair of tangents on $C_1$, where $P$ is any point on the director circle of $C_1$, then the radius of the smallest circle which touches $C_1$ externally and also the two tangents $PA$ and $PB$ is

From points on the straight line $3x-4y+12=0,$ tangents are drawn to the circle $x^2+y^2=4.$ Then the chord of contact passes through a fixed point. The slope of the chord of the circle having this fixed point as its midpoint is

If the tangent at $(1,2)$to the circle $C_1: x^2+y^2=5$ intersects the circle $C_2: x^2+y^2=9$ at $A$and $B$and tangents at $A$ and $B$ to the second circle meet at point $C$, then the coordinates of $C$are given by