Draw a line segment $\mathrm{PQ}$ of $4 \mathrm{cm}$. Draw a perpendicular bisector that cuts line $\mathrm{PQ}$ at point $\mathrm{D}$. Is $\mathrm{PD}=\mathrm{QD}$? Now, we draw a circle whose centre at $\mathrm{D}$ and its radius is $\mathrm{PD}$, and observe that this circle passes through $\mathrm{P}$ and $\mathrm{Q}$.

Use ruler and compass for this question. Construct a circle of radius $4.5 \mathrm{cm}$. Draw a chord. $\mathrm{AB}=6 \mathrm{cm}$. Find the locus of points equidistant from $\mathrm{A}$ and $\mathrm{B}$.
Mark the point where it meets the circle as $\mathrm{D}$. Join $\mathrm{AD}$ and find the locus of points which are equidistant from $\mathrm{AD} \text{and} \mathrm{AB}$. Mark the point where it meets the circle as $\mathrm{C}$.

Use ruler and compass for the question. Construct a circle of radius $4.5 \mathrm{cm}$. Draw a chord $AB=6 \mathrm{cm}$.

Find the locus of points equidistant from $A$ and $B$. Mark the point where it meets the circle as $D$.

A circle of radius $4.5 cm$ is drawn with chord $AB 6 cm$. $D$ is the locus of points of $A$ and $B$. $C$ is the locus of points of $AD$ and $AB$. Join $BC$ and $CD$. Measure and write down the length of side $CD$ of the quadrilateral $ABCD$.​

The angle which cannot be constructed using a ruler and compass only is

With a ruler and compass only, construct the following angle:

$150°$.

Copy $\angle AOB$ shown in the given figure. Using a ruler and compass, construct an angle equal to $2\frac{1}{2}$times $\angle AOB$.