The determination of a line in the plane requires two geometric constraints; among the employed conditions are the pass or membership of a point and angular type (form an angle with another line or circle).
Discuss the angular relation of a given condition to provide a method of obtaining solutions for reducing problems tangency circumference, valid for one or two angular conditions.
The so-called fundamental problem of tangents may occur with respect tangency conditions of a circle, instead of a straight.
Conceptually we can assume that the above is a particular case of this, if we consider the straight as a circle of infinite radius.
In both cases therefore apply similar reasoning for resolution, based on the concepts learned power.
Classically tangencies problems have been studied looking geometric constructions of each case study.
The concepts of power of a point on a circle can address the problems with a unifying approach, so that any tangency or incidences statement generally be reduced to a more generic fundamental problem tangents denominate (PFT).
Along with the concepts of power, Geometry triangle solves proportional means obtaining by known theorems height and Hick.
Before stating these theorems and deduce, recall some basic concepts of proportionality to understand what it is that we can solve with constructs derived from these geometric models.
El concepto de potencia de un punto respecto de una circunferencia se basa en el producto de la mayor por la menor de las distancias de un punto a una circunferencia.
These distance values are given in the string that contains the center of the circle and the point, namely, in diameter containing said point.
Is it possible to generalize this concept to consider other strings passing through the point P?
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.
Los lugares geométricos permiten determinar puntos que satisfacen una determinada condición geométrica. Of interest in the resolution of problems in which metric or geometric restrictions.
Algunos lugares geométricos son elementales y sirven para definir figuras
Geometric transformations can be understood as a set of geometric operations that create a new figure from a previously given, invariants and properties obtained in these. The new figure is called “homologous” or correlative of the original depending on the nature of the transformation of its basic elements.
El concepto de potencia de un punto respecto de una circunferencia permite relacionar las nociones estudiadas en los teorema de Thales y Pitágoras y es la puerta para el estudio de los problemas de tangencias y transformaciones como la inversión.
We will use the concepts of able to arch over a segment on our shows, what is suggested by his review.
This concept is based on the product of two segment and, as discussed, It allows to determine geometrical places of great importance as for example the radical axis of two circles.
Incidence problems trying to identify common elements of two geometric figures; can be defined as special cases of belonging.
Starting from the line and plane elements, We can apply the concepts of duality to analyze the possible problems that may occur.
The ratio between the inscribed angle and the central angle in the circumference allows to obtain a locus of great importance for numerous applications in geometry metric; this is called arc locus capable.
