M L Aggarwal Solutions for Exercise 2: Exercise 16.2

Using a ruler and a pair of compasses only, construct :

a triangle $ABC$, given $AB=4 \mathrm{cm}$, $BC=6 \mathrm{cm}$ and $\angle ABC=90°$.

a circle which passes through the points $A, B$ and $C$ and mark its centre as $O$.

Construct a triangle with sides $3 \mathrm{cm}$, $4 \mathrm{cm}$ and  $5 \mathrm{cm}$. Draw its circumcircle and measure its radius.

Using ruler and compasses only :

Construct a triangle $ABC$ with the following data:

Base $AB=6 \mathrm{cm}$, $AC=5.2 \mathrm{cm}$ and $\angle CAB=60°$.

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

Using ruler and compasses only, construct a triangle $\mathrm{ABC}$ in which $\mathrm{BC}=4 \mathrm{cm}, \angle \mathrm{ACB}=45°$ and the perpendicular from $\mathrm{A}$ on $\mathrm{BC}$ is $2.5 \mathrm{cm}$. Draw the circumcircle of triangle $\mathrm{ABC}$ and measure its radius.

Using ruler and compass only, construct a $∆ABC$ such that $BC=5 \mathrm{cm}$ and $AB=6.5 \mathrm{cm}$ and $\angle ABC=120°$. Construct a cyclic quadrilateral $ABCD$, such that $D$ is equidistant from $AB$ and $BC$.

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

Construct a incircle of a regular hexagon of side $4 \mathrm{cm}$.