Construct incircle and circumcircle of an equilateral $\Delta DSP$ with side $7.5$$\text{cm}$. Measure the radii of both the circles and find the ratio of radius of circumcircle to the radius of incircle.

Distance of chord $\mathrm{AB}$ from the centre of a circle is $8$ $\text{cm}$. Length of the chord $\mathrm{AB}$ is $12$$\text{ cm}$. If the diameter of the circle is $k \mathrm{cm}$ then find $k$.

Diameter of a circle is $26$$\text{ cm}$ and length of a chord of the circle is $24$$\text{ cm}$. If the distance of the chord from the centre is $k \mathrm{cm}$ then find $k$.

Radius of a circle is $34 \text{cm}$ and the distance of the chord from the centre is $30$$\text{ cm}$, if the length of the chord is $k \mathrm{cm}$ then find $k$.

Radius of a circle with centre $O$ is $41$ units. Length of a chord $\mathrm{PQ}$ is $80$ units, if the distance of the chord from the centre of the circle is $k \mathrm{cm}$ then find $k$.

In figure given below, centre of two circles is $O$. Chord $\mathrm{AB}$ of bigger circle intersects the smaller circle in points $\mathrm{P}$ and $\mathrm{Q}$. Show that $\mathrm{AP}=\mathrm{BQ}$

Prove that, if a diameter of a circle bisects two chords of the circle then those two chords are parallel to each other.

Construct $\Delta ABC$ such that $\angle B=100°, BC=6.4, \angle C=50°$ and construct its incircle.

In the figure given, $P$ is the centre of the circle. Chord $AB$ and chord $CD$ intersect on the diameter at the point $E$ If $\angle AEP\cong \angle DEP$ then prove that $AB=CD$.