Dr. SK Goyal Solutions for Chapter: Circle, Exercise 5: INTRODUCTORY EXERCISE 4.5

If the chord of contact of tangents from a point $P$ to a circle passes through $Q.$ If $l_1$ and $l_2$ are the lengths of the tangents from $P$ and $Q$ to the circle, then $PQ$ is equal to

The locus of mid-points of chord of the circle $x^2+y^2=4$ which subtends a right angle at the origin is

The tangents drawn from the origin to the circle $x^2+y^2-2kx-2ry+r^2=0$ are perpendicular, if :

The length of tangent from $\left(0,0\right)$ to the circle $2\left(x^2+y^2\right)+x-y+5=0$ is :

Two perpendicular tangents to the circle $x^2+y^2=a^2$ meet at $P$. Then the locus of $P$ has the equation :

Distances from the origin to the centre of the three circles $x^2+y^2-2\lambda x=c^2$ where $c$ is a constant are in $\mathrm{GP}$. Prove that the lengths of tangents drawn from any point on the circle $x^2+y^2=c^2$ to the three circles are also in $\mathrm{GP}$.

If the length of the tangent from a point $\left(f,g\right)$ to the circle $x^2+y^2=4$ be four times the length of the tangent from it to the circle $x^2+y^2=4x$, show that $15f^2+15g^2-64f+4=0$.

Find the equation of that chord of the circle $x^2+y^2=15$ which is bisected at $\left(3,2\right)$.