Perpendicular from the Centre to a Chord

The perpendicular distance of a chord from the centre of a circle is $6 \mathrm{cm}$. If the length of the chord is $2 \mathrm{cm}$ less than thrice the perpendicular distance, what is the radius of the circle?

In the figure ,$O$ is the centre of the circle of radius $5 \mathrm{cm}$. $OP\perp AB, OQ\perp CD, AB\parallel CD, AB=6 \mathrm{cm}, CD=8 \mathrm{cm}$. Then $PQ$ is:

(Write the answer in $\mathrm{cm}$)

Find the length of a chord which is at a distance of $5 \mathrm{cm}$ from the centre of a circle of radius $13 \mathrm{cm}$. (Write the answer in $\mathrm{cm}$)

In the given figure, $\mathrm{CD}$ is the perpendicular bisector of the chord $\mathrm{AB}.$If $\mathrm{AB}=2 \mathrm{cm}, \mathrm{CD}=4 \mathrm{cm}$ and the radius of the circle is $r \mathrm{cm}$, then find the value of $r$ in decimal.

In the above figure $O$ is the center of the circle. Select the following statements as true and false : $\left(\mathrm{i}\right)$ $\mathrm{AC}=\mathrm{CB}$ $\left(\mathrm{ii}\right)$ $AB=\frac{1}{2}AC$ $\left(\mathrm{iii}\right)$ $AB=2AC$ $\left(\mathrm{iv}\right)$ $OC=\sqrt{O{A}^2-A{C}^2}$ $\left(\mathrm{v}\right)$ $AC=\sqrt{O{A}^2+O{C}^2}$

A $8 \mathrm{cm}$ long chord is drawn in a circle. Whose distance from the centre is $3 \mathrm{cm}$. Find the length of another chord drawn in this circle whose distance from the centre is $4 \mathrm{cm}$. (Write your answer without unit)

A $10 \mathrm{cm}$ long chord is drawn in a circle whose distance from the centre of the circle is $12 \mathrm{cm}$. Find the radius of the circle. (Write your answer without unit)

In the following figure, $O$ is the centre of circle with radius $13 \mathrm{cm}$. If length of $OM$ is $5 \mathrm{cm}$ then find the length of $AB$. (Write your answer without unit)

In the following figure, $O$ is centre of the circle with radius $5 \mathrm{cm}$. Length of the chord of the circle is $AB$ is $6 \mathrm{cm}$. If $OM\perp AB$ then find length of $OM$. (Write your answer without unit)

In the given figure, $O$ is the centre of a circle and diameter $AB$ bisects the chord $CD$ at a point $E$ such that $CE=ED=8 \mathrm{cm}$ and $EB=4 \mathrm{cm}$. The radius of the circle is $r \mathrm{cm}$. The value of $\frac{r}{2}$ is

In the given figure, $CD$ is the diameter of a circle with centre $O$ and $CD$ is perpendicular to chord $AB$. If $AB=12 \mathrm{cm}$ and $CE=3 \mathrm{cm}$, then radius of the circle is $r \mathrm{cm}$. The value of $2r$ is

$AB$ and $CD$ are two chords of a circle such that $AB=6 \mathrm{cm}, \mathrm{CD}=12 \mathrm{cm}$ and $AB\parallel \mathrm{CD}$. If the distance between $AB$ and $CD$ is $3 \mathrm{cm},$ find the radius of the circle.

The perpendicular from the centre of a circle to a chord _____
the chord.

 The distance of a perpendicular from the centre of a circle to the chord if the diameter of the circle is $30 \mathrm{cm}$ and its chord is $24 \mathrm{cm}$.

Two circle of radii $5\mathrm{cm}$ and $3\mathrm{cm}$ are concentric. Calculate the length of a chord of the outer circle which touches the inner circle. 

Two circles with centres $\mathrm{A}$ and $\mathrm{B},$ and radii $5 \mathrm{cm}$ and $3 \mathrm{cm},$ touch each other internally. If the perpendicular bisector of the segment $\mathrm{AB}$ meets the bigger circle in $\mathrm{P}$ and $\mathrm{Q},$ and the length of $\mathrm{PQ}$ is $4\sqrt{k} \mathrm{cm}$. Find $k$.

Two chords $\mathrm{AB}$ and $\mathrm{AC}$ of a circle are equal. Prove that the centre of the circle lies on the bisector of angle $\mathrm{BAG}.$
 

Radius $OA=5 \mathrm{cm}$ and chord $AB=8 \mathrm{cm}$. From the center $O$ the perpendicular radius $OCD$ is drawn on the chord. The measure of the line segment $CD$ will be

The centre $O$ of the circle in above figure whose chord $AB=30 \mathrm{mm}$ and diameter $AC=34 \mathrm{mm}$. The distance of the chord from the centre will be $OD$.