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Some authors have used the term "splitter" in a more general sense, for any line segment that bisects the perimeter of the triangle. Other line segments of this type include the cleavers, which are perimeter-bisecting segments that pass through the midpoint of a triangle side, and the equalizers, segments that bisect both the area and perimeter of a triangle.
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one ...
Because of this construction, the Nagel point is sometimes also called the bisected perimeter point, and the segments AT A, BT B, CT C are called the triangle's splitters. There exists an easy construction of the Nagel point. Starting from each vertex of a triangle, it suffices to carry twice the length of the opposite edge.
The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura (1903-1983). The problem asks for the largest number N ( k ) of nonoverlapping triangles whose sides lie on an arrangement of k lines .
In geometry, a cevian is a line segment which joins a vertex of a triangle to a point on the opposite side of the triangle. [ 1 ] [ 2 ] Medians and angle bisectors are special cases of cevians. The name "cevian" comes from the Italian mathematician Giovanni Ceva , who proved a well-known theorem about cevians which also bears his name.
The chapter on areas includes both trigonometric formulas and Heron's formula for computing the area of a triangle from its side lengths, and the chapter on inequalities includes the ErdÅ‘s–Mordell inequality on sums of distances from the sides of a triangle and Weitzenböck's inequality relating the area of a triangle to that of squares on ...
The theorem follows directly from the fact that the triangles PAC and PBD are similar. They share ∠ DPC and ∠ ADB = ∠ ACB as they are inscribed angles over AB . The similarity yields an equation for ratios which is equivalent to the equation of the theorem given above: P A P C = P B P D ⇔ | P A | ⋅ | P D | = | P B | ⋅ | P C ...
Conway's circle theorem as a special case of the generalisation, called "side divider theorem" (Villiers) or "windscreen wiper theorem" (Polster)) Conway's circle is a special case of a more general circle for a triangle that can be obtained as follows: Given any ABC with an arbitrary point P on line AB.