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The midpoint theorem generalizes to the intercept theorem, where rather than using midpoints, both sides are partitioned in the same ratio. [1] [2] The converse of the theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle.
By Girard's theorem, the sum of the angles of a triangle on a sphere is (+), where is the fraction of the sphere's area enclosed by the triangle. [ 73 ] [ 74 ] In more general spaces, there are comparison theorems relating the properties of a triangle in the space to properties of a corresponding triangle in a model space like hyperbolic or ...
Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction.The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the ...
This fact is known as the Feuerbach conic theorem. The nine point circle and the 16 tangent circles of the orthocentric system. If an orthocentric system of four points A, B, C, H is given, then the four triangles formed by any combination of three distinct points of that system all share the same nine-point circle.
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
The Tennessee Titans interviewed four more candidates Saturday in their search for a new general manager. Tennessee virtually interviewed Colts assistant general manager Ed Dodds, Seattle senior ...
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, = = =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.
Due to the Pythagorean theorem the number () has the simple geometric meanings shown in the diagram: For a point outside the circle () is the squared tangential distance | | of point to the circle . Points with equal power, isolines of Π ( P ) {\displaystyle \Pi (P)} , are circles concentric to circle c {\displaystyle c} .