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A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the sum of the squares of the diagonals (the parallelogram law).
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 ...
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. The triangle formed by the three parallel lines through the three midpoints of sides of a triangle is called its medial triangle.
The three lines connecting the excenters of the given triangle to the corresponding edge midpoints all meet at the mittenpunkt; thus, it is the center of perspective of the excentral triangle and the median triangle, with the corresponding axis of perspective being the trilinear polar of the Gergonne point. [5]
Creating the line through two points; Creating the circle that contains one point and has a center at another point; Creating the point at the intersection of two (non-parallel) lines; Creating the one point or two points in the intersection of a line and a circle (if they intersect)
These are the connected components of the points that would remain after removing all points on lines. [1] The edges or panels of the arrangement are one-dimensional regions belonging to a single line. They are the open line segments and open infinite rays into which each line is partitioned by its crossing points with the other lines.
Given such a configuration the point P is located on the Newton line, that is line EF connecting the midpoints of the diagonals. [1] A tangential quadrilateral with two pairs of parallel sides is a rhombus. In this case, both midpoints and the center of the incircle coincide, and by definition, no Newton line exists.
Therefore, the circumradius of this rhombicosidodecahedron is the common distance of these points from the origin, namely √ φ 6 +2 = √ 8φ+7 for edge length 2. For unit edge length, R must be halved, giving R = √ 8φ+7 / 2 = √ 11+4 √ 5 / 2 ≈ 2.233.