R K Bansal Solutions for Exercise 1: EXERCISE

Given two equal chords $AB$ and $CD$ of a circle, with centre $O$, intersecting each other at point $P$. Prove that $\mathrm{AP}=\mathrm{CP}$.

Given two equal chords $AB$ and $CD$ of a circle, with centre $O$, intersecting each other at point $P$. Prove that $\mathrm{BP}=\mathrm{DP}$.

In a circle of radius $10 \mathrm{cm}, AB$ and $CD$ are two parallel chords of lengths $16 \mathrm{cm}$ and $12 \mathrm{cm}$, respectively. If the distance between the chords (the chords are on the same side of the centre) is $k \mathrm{cm}$, find $k$.

In a circle of radius $10 \mathrm{cm}, \mathrm{AB}$ and $CD$ are two parallel chords of lengths $16 \mathrm{cm}$ and $12 \mathrm{cm}$ respectively. If the distance between the chords, if they are on the opposite sides of the centre is $k \mathrm{cm}$, find $k$.

In the given figure, $O$ is the centre of the circle with radius $20 \mathrm{cm}$ and $\mathrm{OD}$ is perpendicular to $AB$. $\mathrm{AB}=32 \mathrm{cm}$. If the length of $CD$ is $k \mathrm{cm}$, find $k$.

In the given figure, $AB$ and $CD$ are two equal chords of a circle, with centre $O$. $P$ is the mid-point of chord $AB, Q$ is the mid-point of chord $CD$ and $\angle \mathrm{POQ}=150°$. If $\angle \mathrm{APQ}=k°$, find $k$.

In the given figure, $\mathrm{AOC}$ is the diameter of the circle, with centre $O$. Arc $AXB$ is half of arc $BYC$. If $\angle \mathrm{BOC}=k°$, find $k$.

The circumference of a circle, with centre $O$, is divided into three arcs $\mathrm{APB}, \mathrm{BQC}$ and $\mathrm{CRA}$ such that $\frac{arc\mathrm{APB}}{2}=\frac{arc\mathrm{BQC}}{3}=\frac{arc\mathrm{CRA}}{4}$. If $\angle \mathrm{BOC}=p°$, find $p$.