engleski

Semiprogramed analysis of triangles

We observe triangles inscribed in the unit circle centered at the origin, having one vertex and a measure of the corresponding angle fixed. By using software Mathematica, we describe incenters of such triangles as a parametric curve. We show that it is a limacon of Pascal. Furthermore, we consider the extreme values of the inradius and give a new proof of the Euler inequality concerning inradius and circumradius. We, also, give the illustration of our results by using the Sketchpad graphics.

incircle; circumcircle; excircle; limacon of Pascal

nije evidentirano