Search results
Results from the WOW.Com Content Network
The center of the incircle is a triangle center called the triangle's incenter. [1] An excircle or escribed circle [2] of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. [3]
The incenter may be equivalently defined as the point where the internal angle bisectors of the triangle cross, as the point equidistant from the triangle's sides, as the junction point of the medial axis and innermost point of the grassfire transform of the triangle, and as the center point of the inscribed circle of the triangle.
However, Routh's theorem, which goes hand in hand with mass points, uses ratios of lengths to calculate the ratio of areas between a triangle and a triangle formed by three cevians. Special cevians - When given cevians with special properties, like an angle bisector or an altitude , other theorems may be used alongside mass point geometry that ...
For example, the circumcircle and the incircle of the reference triangle are triangle conics. Other examples are the Steiner ellipse which is an ellipse passing through the vertices and having its centre at the centroid of the reference triangle, the Kiepert hyperbola which is a conic passing through the vertices, the centroid and the ...
In geometry, the incircle of the medial triangle of a triangle is the Spieker circle, named after 19th-century German geometer Theodor Spieker. [1] Its center, the Spieker center, in addition to being the incenter of the medial triangle, is the center of mass of the uniform-density boundary of triangle. [1]
Let I be the center of the incircle of triangle ABC, r its radius and F a, F b and F c the three points where the incircle touches the triangle sides a, b and c. Since the (extended) triangle sides are tangents of the incircle it follows that IF a, IF b and IF c are perpendicular to a, b and c.
In triangle geometry, an inellipse is an ellipse that touches the three sides of a triangle. The simplest example is the incircle. Further important inellipses are the Steiner inellipse, which touches the triangle at the midpoints of its sides, the Mandart inellipse and Brocard inellipse (see examples section). For any triangle there exist an ...
In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example, the centroid , circumcenter , incenter and orthocenter were familiar to the ancient Greeks , and can be obtained by simple constructions .