Chhattisgarh Board Solutions for Exercise 10: Exercise – 1

Find the length$\left(\mathrm{cm}\right)$ of the chord of a circle, if radius $13 \mathrm{cm}$ and distance of chord from centre $12 \mathrm{cm}$.

Find the length$\left(\mathrm{cm}\right)$ of the chord of a circle, if radius $15 \mathrm{cm}$ and distance of chord from centre $9 \mathrm{cm}$.

Find the radius of a circle if length of chord and its distance from centre are $8 \mathrm{cm}$ and $3 \mathrm{cm}$ respectively.

Find the radius of a circle if length of chord and its distance from centre are $14 \mathrm{cm}$ and $24 \mathrm{cm}$ respectively.

In the given figure, $\mathrm{PQ}$ is the diameter of a circle. $\mathrm{MN}\perp \mathrm{PQ}$, $\mathrm{PQ}=10 \mathrm{cm}$ and $\mathrm{PR}=2 \mathrm{cm}$, then find the length of $\mathrm{MN}$ in $\mathrm{cm}$?

In the given figure, chord $\mathrm{AB}=18 \mathrm{cm}$ and $\mathrm{PQ}$ is perpendicular bisector of chord $\mathrm{AB}$ which meets the chord on point $\mathrm{M}$. If $\mathrm{MQ}=3 \mathrm{cm}$, then find the radius of the circle in $\mathrm{cm}$?

A circle with centre $\mathrm{O}$ and chords $\mathrm{PQ}, \mathrm{QR}$ such that $\angle \mathrm{PQO}=\angle \mathrm{OQR}=55°$. Prove that $\mathrm{PQ}=\mathrm{QR}$.

$\mathrm{AB}$ and $\mathrm{AC}$ are two equal chords of a circle with centre $\mathrm{O}$. If $\mathrm{OD}\perp \mathrm{AB}$ and $\mathrm{OE}\perp \mathrm{AC}$, then prove that $∆\mathrm{ADE}$ is isosceles triangle.