Embibe Experts Solutions for Chapter: Circles, Exercise 1: Exercise

How the tangent to a circle is a special case of the secant?

Two circles touch externally at $A$. A common tangent $PQ$ to two circles touches the circles at $P$ and $Q$. Then the measure of $\angle PAQ$ is

What sort of a quadrilateral is formed by the tangents at the ends of two perpendicular diameters of a circle?

$∆\mathrm{ABC}$ is isosceles with $\mathrm{AB}=\mathrm{AC}$. The incircle of the $∆\mathrm{ABC}$ touches $\mathrm{BC}$ at $\mathrm{P}$. Prove that $\mathrm{BP}=\mathrm{CP}$.

The rectangle circumscribed about a circle is a square. Prove it.

Identify and write the name of the intersecting lines, secants and tangents in the following figure.

The tangents at $A$ and $B$ of a circle meet at $P$. If $\angle APB=56°$, then what is the value of $\angle PAB$?

In the figure, two tangents $\mathrm{TP} \text{and} \mathrm{TQ}$ are drawn to a circle with centre $\mathrm{O}$ from an external point $\mathrm{T}$. Prove that $\angle \mathrm{PTQ}=2\angle \mathrm{OPQ}$.