O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 1: Exercise

The radius of a circle is $2.5 \mathrm{cm}$. $\mathrm{AB}$ and $\mathrm{CF}$ are two parallel chords  $3.9 \mathrm{cm}$apart. If, $\mathrm{AB}=1.4 \mathrm{cm}$, find $\mathrm{CF}$.

A chord distant $2 \mathrm{cm}$ from the centre of a circle is $18 \mathrm{cm}$ long. If the length of a chord of the same circle which is $6 \mathrm{cm}$ distant from the centre is $k cm$ then find the value of $k$.

In the given Figure $\mathrm{OD}$ is perpendicular to the chord $AB$ of a circle whose centre is $O$. Prove that $\mathrm{CA}=2\mathrm{OD}$.

In Figure $\mathrm{OMNP}$ is a square. A circle drawn with centre $O$ cuts the square in $X$ and $Y$. Prove that: $∆\mathrm{OXM}\cong ∆\mathrm{OYP}$, Hence prove that $\mathrm{NX}=\mathrm{NY}$.

Two equal chords $AB$ and $CD$ of a circle intersect at $P,$show that $\mathrm{AP}=\mathrm{PD} \mathrm{and} \mathrm{BP}=\mathrm{CP}$.

In the given figure shows circle with Centre $O$, with equal chords $\mathrm{AB}$ and $\mathrm{CD};$ $\mathrm{OE}\perp \mathrm{CD}$ at $\mathrm{H}$ and $\mathrm{OF}\perp \mathrm{AB}$ at $\mathrm{G}$. Prove that $\mathrm{EH}=\mathrm{GF}$.

In Figure $C$ is the centre of the circle.$\mathrm{CB}$ bisects the $\angle \mathrm{DBE}$, $\mathrm{CD}\perp \mathrm{PQ}$ and $\mathrm{CE}\perp \mathrm{RS}$. Prove that $\mathrm{PQ}=\mathrm{RS}$.

In the given Figure, $AB$ and $CD$ Are equal chords of a circle whose Centre is $O.$ $\mathrm{OM}\perp \mathrm{AB}$ and $\mathrm{ON}\perp \mathrm{CD}$ prove that $\angle \mathrm{OMN}=\angle \mathrm{ONM}$.