Example 1
If I know P, Q and R, how can I trace the circle inscribed in the triangle PQR?
For example, suppose that P = (−3, 2), Q = (7.5, 5), R = (2, 7.5).

I can find the center of the circle by intersecting two bisectors, and then find its radius by calculating the distance of the center from one of the sides. Direction of PR (see):

Direction of PQ:

Direction of PC (see):

Direction of (QR, QP and) QC:

C, intersection of PC and QC (see):

The radius (CS), distance between C and PQ (see):


The graph with a script. See here.

Example 2:
Human body weight (peso corporeo); 482 Italian males in their twenties, in the year 1990.   (here).
We have seen how to obtain the following histogram and the following elaborations:

We can get (with this version):

Values are rounded to units. The central 50% of the data is in [63, 75], an interval of amplitude 12.  The average weight (of Italian males in their twenties, in the year 1990) is  70.24±1.37 kg,  or  70.3±1.4 kg.