Jose Paul Solutions for Chapter: Chords and Angles of Circles, Exercise 1: EXERCISE 13.1

In the given figure, $AB=8 \mathrm{cm}, OP=3 \mathrm{cm}$. If the radius $OA$ is $k \mathrm{cm}$, then find the value of $k$.

From the given data, find the length of the segment as required.

$PQ=12 \mathrm{cm}, OP=10 \mathrm{cm}$. If the distance of $OM$ is $k \mathrm{cm}$ then find $k$.

$\overline{PQ}=30 \mathrm{cm}, \overline{OM}=8 \mathrm{cm}$. If the radius $OP=k \mathrm{cm}$, then find the value of $k$.

In the given figure, $\overline{AB}=\overline{CD}, \overline{OP}=5 \mathrm{cm}$ and if $\overline{OM}=k \mathrm{cm}$, then find $k$.

From the given data, find the length of the segment as required.

$\overline{PQ}=7 \mathrm{cm}, \overline{OA}=\overline{OB}$. If $RS=k \mathrm{cm}$ then find $k$.

The diameter and a chord of a circle have a common endpoint as shown in the figure. If the length of the diameter is $40 \mathrm{cm}$, the length of the chord is $24 \mathrm{cm}$ and the distance of midpoint of the chord from the centre is $k \mathrm{cm}$ then find $k$.

A chord whose midpoint is $15 \mathrm{cm}$away from the centre of the circle is $16 \mathrm{cm}$ long. If the radius of the circle is $r \mathrm{cm}$, then find the value of $r$.

Given a circle with centre $P. P$ is the midpoint of $MN$. $MN$ is perpendicular to $\overline{BC}$  as well as $\overline{AD}$. Prove that  $\overline{ABCD}$ is a rectangle.