# Metric geometry : Investment beam circumferences

Transformation through investment in geometric shapes grouped elements can be of interest to use the investment as a tool for analysis in complex problems. In this case study transforming “beams circumferences corradicales” through various investments that transform. Later these transformations need to solve the problem “Apolonio” (circumference with three tangency constraints) o la “Generalization of the problem of Apollonius” (circumferences with three angular restrictions).

# Determinación de un segmento conocido su punto medio [Solución]

Al plantear un problema de geometría métrica podemos abordar su resolución con diferentes estrategias. para ilustrar uno de estos métodos vamos a resolver el de determinar un segmento del que se conoce su punto medio junto con otras restricciones adicionales.

En particular analizaremos el caso en el que los extremos del segmento se encuentran situados sobre dos circunferencias coplanarias de radio arbitrario.

# Metric geometry : Make hyperbolic circles

When defining a beam circumferences as an infinite set simply fulfilling a restriction on the power, sorted the beams depending on the relative position of its elements.

Hyperbolic circumferences beams are among these families circumferences. Of the three existing (Elliptical, parabolic and hyperbolic) are those that offer greater difficulty in its conceptualization to come not defined waypoints. We will see how to determine elements that belong to them as it did in the previous cases.

# Metric geometry : Haz elíptico de circunferencias

When defining a beam circumferences as an infinite set simply fulfilling a restriction on the power, sorted the beams depending on the relative position of its elements.

Circumferences elliptical beams are among these families circumferences. We will see how to determine elements that belong.