EXERCISE

The radius of a circle is $8 \mathrm{cm}$ and the length of one of its chords is $12 \mathrm{cm}$. Find the distance of the chord from the centre.

If the length of a chord which is at a distance of $5 \mathrm{cm}$ from the centre of a circle of radius $10 \mathrm{cm}$ is $k \mathrm{cm}$, find the value of $k$ nearest to two decimal places.

Find the length of a chord which is at a distance of $4 \mathrm{cm}$ from the centre of the circle of radius $6 \mathrm{cm}$.

An equilateral triangle of side $9 \mathrm{cm}$ is inscribed in a circle. If the radius of the circle is $k\sqrt{k} \mathrm{cm}$, then find the value of $k$.

The lengths of two parallel chords of a circle are $6 \mathrm{cm}$ and $8 \mathrm{cm}$. If the smaller chord is at a distance of $4 \mathrm{cm}$ from the centre, what is the distance of the other chord from the centre?

Two chords $AB, CD$ of lengths $5 \mathrm{cm},11 \mathrm{cm}$ respectively of a circle are parallel. If the distance between $AB$ and $CD$ is $3 \mathrm{cm}$ and the radius of the circle is $\frac{\sqrt{k}}{2} \mathrm{cm}$, then find the value of $k$.

Prove that two different circles cannot intersect each other at more than two points.

Two chords $AB$ and $CD$ of lengths $5 \mathrm{cm}$ and $11 \mathrm{cm}$ respectively of a circle are parallel to each other and are opposite side of its centre. If the distance between $AB$ and $CD$ is  $6 \mathrm{cm},$ if the radius of the circle is $\frac{k\sqrt{k}}{2} \mathrm{cm}$, then find the value of $k$.