Jitender Gupta and Divya Malik Solutions for Exercise 3: ARCHIVES (Last 8 Years)

Construct a regular hexagon of side $5 \mathrm{cm}$. Construct a circle circumscribing the hexagon. All traces of construction must be clearly shown.

Construct a $△ABC$ with $BC=6.5 \mathrm{cm}, AB=5.5 \mathrm{cm}$ and $AC=5 \mathrm{cm}$. Construct the incircle of the triangle. Measure and record the radius of the incircle.

Using a ruler and a compass only, construct a $△ABC$ in which $AB=3.5 \mathrm{cm}, BC=6 \mathrm{cm}$ and $\angle ABC=120°$. 

Using a ruler and a compass only, construct a $△ABC$ in which $AB=3.5 \mathrm{cm}, BC=6 \mathrm{cm}$ and $\angle ABC=120°$. Draw a circle with $BC$ as diameter. Find a point $P$ on the circumference of the circle which is equidistant from $AB$ and $AC$. 

Using a ruler and a compass only, construct a $△ABC$ in which $AB=3.5 \mathrm{cm}, BC=6 \mathrm{cm}$ and $\angle ABC=120°$. Draw a circle with $BC$ as diameter. Find a point $P$ on the circumference of the circle which is equidistant from $AB$ and $AC$. Measure $\angle BCP$.

Construct a $△ABC$  in which base $BC=6 \mathrm{cm}, AB=5.5 \mathrm{cm}$ and $\angle ABC=120°$ . Construct a circle circumscribing the $△ABC$.

Construct a $△ABC$  in which base $BC=6 \mathrm{cm}, AB=5.5 \mathrm{cm}$ and $\angle ABC=120°$ . Construct a circle circumscribing the $△ABC$. Draw a cyclic quadrilateral $ABCD$, so that $D$ is equidistant from $B$ and $C$.

Draw a circle of radius $3.5 \mathrm{cm}$. Mark a point $P$ outside the circle at a distance of $6 \mathrm{cm}$ from the centre. Construct two tangents from $P$ to the given circle. Measure and write down the length of one tangent.