Question

Construct a triangle PQR in which PQ=QR=RP=5.7 cm.
Draw the incircle of the triangle and measure its radius.

Answer 1

Steps of construction :

$\left(i\right)$ Draw a line segment $PQ=5.7cm$

$\left(ii\right)$ Taking $Q$ as the centre, draw an arc $5.7cm$ from $Q$ with the help of a compass

$\left(iii\right)$ Again with the help of a compass, draw another arc of $5.7cm$ from $P$ as a centre which intersects the previous arc made by $Q$

$\left(iv\right)$ Mark the intersection point as $R$ and join it to both $P$ and $Q$ respectively

$\left(v\right)$ Thus the required triangle $RPQ$ is obtained

$\left(vi\right)$ Now, from $P$ and $Q$ cut the bisector of $\angle P$ and $\angle Q$, which intersect each other at point $O$

$\left(vii\right)$ Taking $P$ as a centre, draw an incircle which touches all the three sides of $\angle RPQ$