CHAPTER EXERCISE

Draw a circle of radius $4 \mathrm{cm}$. Mark a point A outside the circle. Draw the tangents to the circle from point A, without using the centre of the circle.

Using a ruler and a pair of compasses only, construct a $∆\mathrm{ABC}$, given $\mathrm{AB}=4 \mathrm{cm}, \mathrm{BC}=6 \mathrm{cm} \mathrm{and} \angle \mathrm{ABC}=90°$and a circle that passes through the points $\mathrm{A}, \mathrm{B} \mathrm{and} \mathrm{C}$ and mark its centre as $\mathrm{O}$.

Construct the circumcircle of a triangle whose sides are $5 \mathrm{cm}, 6 \mathrm{cm} \mathrm{and} 8 \mathrm{cm}$.

Draw a triangle with sides $5.5 \mathrm{cm}, 6 \mathrm{cm} \mathrm{and} 6.5 \mathrm{cm}$. Construct its circumcircle.

Construct a circumscribing circle of an equilateral triangle of side $4 \mathrm{cm}$.

Use a ruler and a pair of compasses to construct a $△ABC$, in which $BC=4.2 \mathrm{cm}$, $\angle ABC=60°$ and $AB= 5 \mathrm{cm}$. Construct a circle of radius $2 \mathrm{cm}$ to touch both the arms of $\angle ABC$of $△ABC$.

Construct a regular hexagon of side $4 \mathrm{cm}$. Construct a circle circumscribing the hexagon.

Construct a regular hexagon of side $6 \mathrm{cm}$ and construct a circle in the regular hexagon. Mark its incentre as $I$.