Search results
Results from the WOW.Com Content Network
Secant-, chord-theorem. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: . Intersecting secants theorem: For a point outside a circle and the intersection points , of a secant line with the following statement is true: | | | | = (), hence the product is independent of line .
The circle is an instance of a conic section and the nine-point circle is an instance of the general nine-point conic that has been constructed with relation to a triangle ABC and a fourth point P, where the particular nine-point circle instance arises when P is the orthocenter of ABC.
A polygon whose vertices are concyclic is called a cyclic polygon, and the circle is called its circumscribing circle or circumcircle. All concyclic points are equidistant from the center of the circle. Three points in the plane that do not all fall on a straight line are concyclic, so every triangle is a cyclic polygon, with a well-defined ...
For example, cubes have 12 edges, but 9 measurements are enough to decide if a polyhedron of that combinatorial type is congruent to a given regular cube. Congruent triangles on a sphere Main articles: Solving triangles § Solving spherical triangles , and Spherical trigonometry § Solution of triangles
CLP problems generally have 4 solutions. The solution of this special case is similar to that of the CPP Apollonius solution. Draw a circle centered on the given point P; since the solution circle must pass through P, inversion in this [clarification needed] circle transforms the solution circle
In geometry, a set of Johnson circles comprises three circles of equal radius r sharing one common point of intersection H.In such a configuration the circles usually have a total of four intersections (points where at least two of them meet): the common point H that they all share, and for each of the three pairs of circles one more intersection point (referred here as their 2-wise intersection).
Consider a solution circle of radius r s and three given circles of radii r 1, r 2 and r 3. If the solution circle is externally tangent to all three given circles, the distances between the center of the solution circle and the centers of the given circles equal d 1 = r 1 + r s, d 2 = r 2 + r s and d 3 = r 3 + r s, respectively.
In geometry, the power center of three circles, also called the radical center, is the intersection point of the three radical axes of the pairs of circles. If the radical center lies outside of all three circles, then it is the center of the unique circle (the radical circle) that intersects the three given circles orthogonally; the construction of this orthogonal circle corresponds to Monge ...