Question

Construct the incentre of $△ABC$ with $AB=7cm,\angle B={50}^{\circ }$ and $BC=6cm$. Also draw the incircle and measure its inradius

Answer 1

Step $1$ : Draw the $△ABC$ with the given measurements.
Step $2$ : Construct the angle bisectors of any two angles ($A$ and $B$) and let them meet at $I$. Then $I$ is the incentre of $△ABC$.
Step $3$ : With $I$ as an external point drop a perpendicular to any one of the sides to meet at $D$.
Step $4$ : With $I$ as centre and $ID$ as radius draw the circle. This circle touches all the sides of the triangle.
$Inradius=1.8cm$