Graphic PIZiadas

Graphic PIZiadas

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Metric geometry: Circunferencias con condiciones angulares. Problema I

problema angularGeometric problems can be addressed with different strategies to simplify the analysis and resolution. We can usually fit them into families well structured problems specific solutions to suit each particular problem.

Here is a basic problem in geometry “dress” or “adapted” to a technological application, suppose particularly for defining a part geometric conditions need angular constraints given by.

Problem Statement

Complete development of the part shown in the drawings, knowing that the circle c is tangent to c1, passes through the point P and intersects with an angle of 45 ° to the line r.

Enunciado problema geométrico

Sketch for drawing geometric statement of the problem

Facts and figures

To resolve the problem we will provide part of the data graphically. So, in this case, would:

Enunciado problema geométrico

Statement geometric problem

Concentric circles with c1 are not relevant and can do without them.

Statement analysis and graphical data we see that we must complete the figure by determining a circle has three geometric constraints:

  • Pass (or pertenece) by point P
  • Form angle (45) with The straight r
  • This is tangent to circumference c1.

We see that we must determine the circumference is restricted by a number of conditions identical to the number of data necessary for defining (Two center and one radio), and furthermore that these data are redundant in (linear combination) and therefore are independent of each other, so that this circumference is parametrically determined or, which is the same, the problem is correctly proposed.

The reader is allowed a first analysis of the problem.

We suggest trying to turn the corner in terms of conditions isogonalidad (angle equal) in particular tangents to try to reduce the problem to which we have called “Fundamental Problem Tangencies“.

You can see the solution here