Search results
Results from the WOW.Com Content Network
Each median of a triangle passes through the triangle's centroid, which is the center of mass of an infinitely thin object of uniform density coinciding with the triangle. [1] Thus, the object would balance at the intersection point of the medians.
The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). [6] The centroid divides each of the medians in the ratio 2 : 1 , {\displaystyle 2:1,} which is to say it is located 1 3 {\displaystyle {\tfrac {1}{3}}} of the distance from each side to the opposite ...
In geometry, the Lemoine point, Grebe point or symmedian point is the intersection of the three symmedians (medians reflected at the associated angle bisectors) of a triangle. Ross Honsberger called its existence "one of the crown jewels of modern geometry". [1] In the Encyclopedia of Triangle Centers the symmedian point appears as the sixth ...
In a triangle, four basic types of sets of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors: A triangle's altitudes run from each vertex and meet the opposite side at a right angle. The point where the three altitudes meet is the orthocenter.
The three medians intersect in a single point, the triangle's centroid or geometric barycenter. The centroid of a rigid triangular object (cut out of a thin sheet of uniform density) is also its center of mass: the object can be balanced on its centroid in a uniform gravitational field. [30]
In the diagram, the medians (in black) intersect at the centroid G. Because the symmedians (in red) are isogonal to the medians, the symmedians also intersect at a single point, L. This point is called the triangle's symmedian point, or alternatively the Lemoine point or Grebe point.
For 3 (non-collinear) points, if any angle of the triangle formed by those points is 120° or more, then the geometric median is the point at the vertex of that angle. If all the angles are less than 120°, the geometric median is the point inside the triangle which subtends an angle of 120° to each three pairs of triangle vertices. [ 10 ]
The center of the van Lamoen circle is point () in Clark Kimberling's comprehensive list of triangle centers. [1]In 2003, Alexey Myakishev and Peter Y. Woo proved that the converse of the theorem is nearly true, in the following sense: let be any point in the triangle's interior, and ′, ′, and ′ be its cevians, that is, the line segments that connect each vertex to and are extended until ...