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 $△ABC$
(1) Draw a line segment $BC=8cm$
(2) Draw an arc of radius $=8cm$ taking $B$ as centre.
(3) Draw another arc of radius $=8cm$ taking $B$ as centre
(4) Draw another arc of radius $=8cm$ taking $C$ as centre with intersects the previous arc at a point $A$.
(5) Join $AB$ and $AC$.
Thus the required $△ABC$ is constructed.
Construction of incircle of $△ABC$
(1) Draw $BP$ and $CQ$ the bisectors of angles, $\angle B$ and $\angle C$ respectively and which intersect each other at point $C$.
(2) Draw $ORbotBC$ which intersects $BC$ at $L$.
(3) 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.
(4) Measure the radius $OL$ which is $2.3cm$. Thus the required incircle is constructed and its radius $=2.3cm$