Search results
Results From The WOW.Com Content Network
A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region.
When the outer Soddy circle has negative curvature, its center is the isoperimetric point of the triangle: the three triangles formed by this center and two vertices of the starting triangle all have the same perimeter. [4] Triangles whose outer Soddy circle degenerates to a straight line with curvature zero have been called "Soddyian triangles ...
A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides. The sum can be computed directly using the definition of angle based on the dot product and trigonometric identities , or more quickly by reducing to the two-dimensional case and using Euler's identity .
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);
In the case in which the original triangle has no angle greater than 120°, this point is also the Fermat point. The Apollonius point is the point of concurrence of three lines, each of which connects a point of tangency of the circle to which the triangle's excircles are internally tangent, to the opposite vertex of the triangle.
Two triangles are said to be poristic triangles if they have the same incircle and circumcircle. Given a circle with Center O and radius R and another circle with center I and radius r, there are an infinite number of triangles ABC with Circle O(R) as circumcircle and I(r) as incircle if and only if OI 2 = R 2 − 2Rr. These triangles form a ...
Such a pair of sides may also be said to form an angle of zero. A triangle with a zero angle is impossible in Euclidean geometry for straight sides lying on distinct lines. However, such zero angles are possible with tangent circles. A triangle with one ideal vertex is called an omega triangle. Special Triangles with ideal vertices are:
The difference in area for an equilateral triangle is small, just over 1%, [2] but as Howard Eves pointed out, for an isosceles triangle with a very sharp apex, the optimal circles (stacked one atop each other above the base of the triangle) have nearly twice the area of the Malfatti circles. [3] In fact, the Malfatti circles are never optimal.