How to construct a circle inscribed in a triangle

A circle can be inscribed in any triangleregardless of the lengths of its sides and angles. The algorithm for constructing such a circle is very simple and involves just two steps.

You will need

• A compass, protractor, ruler, pencil

Instruction

1. First you need to find the future center of the inscribed circle. In any triangle, he will be at the point of intersection of the bisectors. Therefore, the first step is the construction of the circle will be conducting the bisectors of the angles of your triangle (it is sufficient to use only two angles). For this you will need to divide the angles in half with the help of a protractor and the vertex opposite rays to the sides or just before crossing each other.
2. The second step is the determination of the radius of the inscribed circle. To do this, from the point of intersection of the bisectors will need to be perpendicular to one (any) of the sides of the triangle. The length of the resulting segment will be equal to the desired radius. After finding this value, you can safely put the compass in the point of intersection of bisectors (the center) and build a circle of the desired radius.
3. If you need not just to construct the inscribed circle and find its radius, then this can easily be done through the following formula: r = S : p, where S is the area of trianglea, and p is its properietor (the sum of the lengths of all three sides, divided into two).