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.
We can assume that the player taking the shot has enough power to do it from any point of his career, making it the most suitable one that offers wider viewing angle of the goal as shown below.
To simplify the statement, without diminishing the generality of the problem, assume that the player is at a point P the field and runs parallel to the band (in the direction d). The goal will be determined by the segment AB.
The player's position will allow you to see the goal under a certain angle “alfa“. Our problem is therefore to find a new path point “d” since this angle is maximum.
In reviewing the concepts of “arc able” on a segment, we can conclude that this point will be the one that belongs to a circle through the points A and B, which in turn is tangent to the line d so that its diameter is minimum.
The line AB will radical axis all the circles through these points, whereas straight “d” it will be all that are tangent to this line. Point Cr intersection of the two lines will have the same power for which pass through A and B, and the tangents to “d“, so we can determine this power value that is the distance to the solution.
The figure has been resolved with a diameter auxiliary circle AB. Power from Cr is equal to the square segment that passes through the tangent point T. The point solution, S, this length to be farther Cr.
Conic as Locus Centers Circumferences Tangents We have seen that the study of conic can be made from different geometric approaches. En particular, to start analyzing conic we have defined as the ellipse locus, we said that:
Ellipse is the locus of points in a plane whose sum […]
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. Para determinar dicho eje será necesario por lo […]
Metric geometry : Generalization of the concept of “Power” 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 […]
Power Concepts [ Prezi ] The concept of power is fundamental to solving problems in a structured way and generalization of tangency where angularity.
This concept, initially apply the fundamental problem of tangents, nos permitirá utilizar un proceso sistemático de […]