# The robustness of dynamic geometric constructions with Geogebra: Polar of a point of a circle

The study of the disciplines of classical geometry can be reinforced by using tools that allow constructions that can be changed dynamically: variational constructions.
The tool “Geogebra” It will serve to illustrate these concepts and demonstrate the importance of detailed knowledge of geometric relationships to ensure the robustness of the buildings we use in geometric reasoning, as, sometimes, some constructions may lose their validity.

# Metric geometry : Obtaining the radical axis of two circles

The two circumferences radical axis is ellugar locus of points of a plane with equal power on two circles.

Is a straight line having a direction perpendicular to the centerline of the circumferences. To determine this axis is therefore necessary to know a single crossing point.

# The problem with football

A curious problem, I usually suggest to my students in class, where we can use geometric knowledge learned by studying the concept of power, is to determine the optimal position of shooting a soccer goal from a given path.

# Metric geometry : Radical axis of two circles

The loci used to determine the solution of problems with geometric constraints. Among the conditions used are the angular nature and among them the orthogonality.
Given two circles, simply infinite set of circles that intersect orthogonally are grouped in a set called beam circumferences corradicales; These circles are centered on a line called the radical axis.