Draw a right triangle whose hypotenuse is $10 \mathrm{cm}$ and one of the legs is $8 \mathrm{cm}$. Locate its incentre and also draw the incircle.

In the figure, $AB$ is parallel to $CD$. If the measure of $\angle x$ is $k°$, then find the value of $k$.

$ABCD$ is a square, diagonals $AC$ and $BD$ meet at $O$. The number of pairs of congruent triangles with vertex $O$ are

In the figure, $O$ is the centre of the circle and $\angle ACB=40°$ then $\angle AOB=$

In the 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

In the figure, $PQRS$ and $PTVS$ are two cyclic quadrilaterals, If $\angle QRS=100°$, then $\angle TVS=$

In the figure, $ABCD$ is a cyclic quadrilateral in which $DC$ produced to $E$ and $CF$ is drawn parallel to $AB$ such that $\angle ADC=80°$ and $\angle ECF=20°,$ then $\angle BAD=$?

Construct the incentre of $∆ABC$ with $AB=6 \mathrm{cm}, \angle B={65}^{\circ }$ and $AC=7 \mathrm{cm}$ Also draw the incircle and measure its radius.