Neha Tyagi and Amit Rastogi Solutions for Chapter: Circles, Exercise 2: Exercise

The length of tangent from an external point $\mathrm{P}$ on a circle with centre $\mathrm{O}$ is always less than $\mathrm{OP}$.

The angle between two tangents to a circle may be $0°$.

If angle between two tangents drawn from a point $P$ to a circle of radius $a$ and centre $O$ is $90°$, then $OP=a\sqrt{2}$.

If angle between two tangents drawn from a point $P$ to a circle of radius $a$ and center $O$ is $60°$, then $OP=a\sqrt{3}$.

The tangent to the circumcircle of an isosceles $∆ABC$ at $A$, in which $AB=AC$, is parallel to $BC$.

If a number of circles touch a given line segment $PQ$ at a point $A$, then their centres lie on the perpendicular bisector of $PQ$.

If a number of circles pass through the end points $P$ and $Q$ of a line segment $PQ$, then their centres lie on the perpendicular bisector of $PQ$.

$AB$ is a diameter of a circle and $AC$ is its chord such that $\angle BAC=30°$. If the tangent at $C$ intersects $AB$ extended at $D$, then $BC=BD$.