Question

Construct an equilateral $\Delta DEF$ whose one side is $5.5$ cm. Construct an incircle to this triangle.

Answer 1

Steps of Construction

1. Construct a line segment $BC=5.5$ cm.

2. Taking B and C as centres and $5.5$ cm radius construct two arcs which intersect each other at point A.

3. Now join AB and AC.

4. Construct the perpendicular bisectors of $\angle B$ and $\angle C$ which intersect each other at the point I.

5. From the point I construct IL which is perpendicular to BC.

6. Taking I as Centre and IL as radius construct a circle which touches the sides of $\Delta$ABC internally.

This is the required incircle.

5. From the point I construct IL which is perpendicular to AB.

6. Taking I as Centre and IL as radius construct a circle which touches the sides of $\Delta$ABC internally.

By measuring the required incircle the radius is $1.6$ cm.