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In classical geometry, the bisection is a simple compass and straightedge construction, whose possibility depends on the ability to draw arcs of equal radii and different centers: The segment is bisected by drawing intersecting circles of equal radius , whose centers are the endpoints of the segment. The line determined by the points of ...
Concurrent lines. In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point. The set of all lines through a point is called a pencil, and their common intersection is called the vertex of the pencil. In any affine space (including a Euclidean space) the set of lines parallel to a given line ...
Cevian. In geometry, a cevian is a line segment which joins a vertex of a triangle to a point on the opposite side of the triangle. [1][2] Medians and angle bisectors are special cases of cevians. The name "cevian" comes from the Italian mathematician Giovanni Ceva, who proved a well-known theorem about cevians which also bears his name.
The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC: and conversely, if a point D on the side BC of ABC divides BC in the same ratio as the sides AB and AC, then AD is the angle bisector of angle ∠ A.
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. It is a special case of an arc, with zero curvature. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both ...
Intersecting chords theorem. In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.