G Tewani Solutions for Chapter: Circles, Exercise 2: DPP

Chord $\mathrm{AB}$ of the circle $x^2+y^2=100$ passes through the point $\left(7, 1\right)$ and subtends an angle of $60°$ at the circumference of the circle. If $m_1$ and $m_2$ are the slopes of two such chords, then the value of $m_1{m}_2$ is.

$P$ and $Q$ are the two points on a line passing through $\left(2,4\right)$ and having slope $m$. If a line segment $AB$ subtends a right angle at $P$ and $Q,$ where $A=\left(0,0\right)$ and $B=\left(6,0\right),$ then range of values of $m$ is

In the $\mathrm{xy}-$ plane, the length of the shortest path from $\left(0,0\right)$ to $\left(12,16\right)$ that does not go inside the circle ${\left(\mathrm{x}-6\right)}^2+{\left(\mathrm{y}-8\right)}^2=25.$

Triangle $\mathrm{ABC}$ is right-angled at $A$. The circle with center $A$ and radius $\mathrm{AB}$ cuts $\mathrm{BC}$ and $\mathrm{AC}$ internally at $D$ and $E$, respectively. If  $\mathrm{BD}=20$ and $\mathrm{DC}=16$ then the length $\mathrm{AC}$ equals

All chords through an external point to the circle $x^2+y^2=16$  are drawn having length $l$ which is a positive integer. The sum of the squares of the distances from the center of the circle to these chords is

The line $3x+6y=k$ intersects the curve $2x^2+2xy+3y^2=1$ at points $A$ and $B$. The circle on $\mathrm{AB}$ as diameter passes through the origin. The possible value/values of $k$ is/are

Consider the circle $x^2+y^2-8x-18y+93=0$ with center $C$ and point $P\left(2, 5\right)$ outside it. From the point $P$, tangents $PQ$ and $PR$ are drawn to the circle with $S$ as the midpoint of $QR$. The line joining $P$ to $C$ intersects the given circle at $A$ and $B$. Which of the following hold(s) good?

Consider two circles $C_1:x^2+y^2-1=0$ and $C_2:x^2+y^2-2=0$. Let $A\left(1,0\right)$ be a fixed point on the circle $C_1$ and $B$ be any variable point on the circle $C_2$. The line $BA$ meets the curve $C_2$ again at $C$. Which of the following is/are correct?