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Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter (the center of its incircle). There are either one, two, or three of these for any given triangle. A line through the incenter bisects one of the area or perimeter if and only if it also bisects the other. [12]
This parallel also intersects the black line m at E, defining one end of the line segment. Create two lines (in green), AC and AD, that each pass through the given circle's center. These green lines intersect the given circle at points G and F, respectively. Line FG (in blue) intersects the line m at H, defining the other endpoint of the line ...
A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry , a line segment is often denoted using an overline ( vinculum ) above the symbols for the two endpoints, such as in AB .
Other concurrencies of a tangential quadrilateral are given here. In a cyclic quadrilateral, four line segments, each perpendicular to one side and passing through the opposite side's midpoint, are concurrent. [3]: p.131, [5] These line segments are called the maltitudes, [6] which is an abbreviation
A ray with a terminus at A, with two points B and C on the right. Given a line and any point A on it, we may consider A as decomposing this line into two parts. Each such part is called a ray and the point A is called its initial point. It is also known as half-line, a one-dimensional half-space. The point A is considered to be a member of the ray.
In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...
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The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.