Question

Construct the incircle of the equilateral triangle whose one side is $8cm$.

Answer 1

Given - An equilateral triangle $ABC$ in which $AB=BC=CA=8cm$.
Required - To construct the given triangle $ABC$ and to draw incircle of it.
Construction of $△ABC$-
$\left(1\right)$ Draw a line segment $BC=8cm$.
$\left(2\right)$ Draw a arc of radius $=8cm$ taking $B$ as centre.
$\left(3\right)$ Draw another arc of radius $=8cm$ taking $B$ as centre.
$\left(4\right)$ Draw another arc of radius $=8cm$. taking $C$ as centre with intersects the previous arc at a point $A$.
$\left(5\right)$ Join $AB$ and $AC$.
Thus the require $△ABC$ is constructed.
Construction of incircle of $△ABC$.
$\left(1\right)$ Draw $BP$ and $CQ$ the bisectors of angles $\angle B$ and $\angle C$ respectively and which intersect each other at point $O$.
$\left(2\right)$ Draw $OR\perp BC$ which intersects $BC$ at $L$.
$\left(3\right)$ Taking $O$ as centre and $OL$ as radius draw a circle which touches the sides $AB,BC$ and $CA$ at points $N,L$ and $M$ respectively.
$\left(4\right)$ Measure the radius $OL$ which is $2.3cm$.
Thus the required incircle is constructed and its radius $=2.3cm$.