# How to construct a incircle pentagon?

1
by anuchandrel

2014-08-17T23:28:28+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
We draw the pentagon first. Let its side be S.

We have to draw the incircle. that incircle touches the sides tangentially at one point and that point is the center of the side. If we draw a perpendicular from the center of the polygon on to the side, it meets the side at the center of the side.
That perpendicular is called apothem.   The APOTHEM is the radius of incircle.

So we have a triangle (Isosceles) with two radii and drawn at two ends of the side, and the side itself.
Now with the apothem, half of side and one radius we have a right angle triangle.

Radius = apothem = a =  1/2  S  cot π/5  =  0.6882  S

From the center of pentagon, draw a circle of radius 0.6882 * Side. That is the INCIRCLE.