B Nirmala Shastry Solutions for Exercise 1: EXERCISE 14A

The length of the common chord $AB$ of two intersecting circles is $18 \mathrm{cm}$. If the diameters of the circles are $82 \mathrm{cm} \mathrm{and} 30 \mathrm{cm}$, calculate the distance between the centres.

In the given circle with centre $O$, $\mathrm{AD}=\mathrm{DB}=16 \mathrm{cm}$ and $\mathrm{DE}=8 \mathrm{cm}$. Find the radius of the circle.

In the given figure, $AD$ is the chord of the larger of the two concentric circles and $BC$ is the chord of the smaller circle. Prove that $AB=CD$.

Triangle $ABC$ is inscribed in a circle with centre $O, AB=AC, OP\perp AB$ and $OQ\perp AC$. Prove that $PB=QC$.

$ABCD$ is a square, $C$ is the centre of the circle. Prove that $AP=AR$.

In the figure given above, $AB$ and $CD$ are two parallel chords and $O$ is the centre. If the radius of the circle is $15 \mathrm{cm}$, find the distance $MN$between the two chords of length $24 \mathrm{cm}$ and $18 \mathrm{cm}$ respectively.

In the given figure, $O$ is the centre of the circle. $AB$ and $CD$ are two chords of the circle. $OM$ is perpendicular to $AB$ and $ON$ is perpendicular to $CD$. $\mathrm{AB}=24 \mathrm{cm}, \mathrm{OM}=5 \mathrm{cm}, \mathrm{ON}=12 \mathrm{cm}$. Find the radius of the circle.

In the given figure, $O$ is the centre of the circle. $AB$ and $CD$ are two chords of the circle. $OM$ is perpendicular to $AB$ and $ON$ is perpendicular to $CD$. $\mathrm{AB}=24 \mathrm{cm}, \mathrm{OM}=5 \mathrm{cm}, \mathrm{ON}=12 \mathrm{cm}$. Find the length of chord $CD$.