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

The distance between the centres of two circles with radius $8 cm$ and $3 cm$ is $13 cm$. What is the length of the direct common tangent to two circles?

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

$A$ and $B$ are two points on the circumference of a circle with centre $O$. Tangent at $A$ to the circle meets $BO$ produced at $P$. If $\angle APB=40°$, then what is the value of $\angle OAB$?

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 $\angle \mathrm{PTQ}=2\angle \mathrm{OPQ}$.

Write whether the two straight lines can be parallel or not in the case of 'Two tangents of the circle'.

Prove that a chord of a circle make equal angles with the tangents at its ends.

$AB$ is a diameter of a circle with centre $O$. The tangent at $P$ to the circle intersects $AB$ produced at $Q$. If $\angle AQP=40°$, then what is the value of $\angle APQ$?

The length of the direct common tangent of two circles with radius $12 cm$ and $4 cm$ is $15 cm$. Find the distance between the centres of the circles.