Embibe Experts Solutions for Chapter: Circles, Exercise 1: Karnataka Board-2020

Prove that if two circles touch each other externally, then their centres and the point of contact are collinear.

A straight line which passes through two points on a circle is 

Prove that the lengths of tangents drawn from an external point to a circle are equal.

In the given figure $PQ \& RS$ are two parallel tangents to a circle with centre $O$ and another tangent $AB$ with point of contact $C$ intersecting $PQ$ at $A$ and $RS$ at $B$. Prove that $\angle AOB=90°$.

Prove that ''the lengths of tangents drawn from an external point to a circle are equal''.

In the figure, $\mathrm{O}$ is the centre of a circle, $\mathrm{AC}$ is a diameter. If $\angle \mathrm{ACB} = 50°$, then find the measure of $\angle \mathrm{BAC}$(in $°$).