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  2. Bisection - Wikipedia

    en.wikipedia.org/wiki/Bisection

    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 ...

  3. Angle bisector theorem - Wikipedia

    en.wikipedia.org/wiki/Angle_bisector_theorem

    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.

  4. Cevian - Wikipedia

    en.wikipedia.org/wiki/Cevian

    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.

  5. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    An angle bisector of a triangle is a straight line through a vertex that cuts the corresponding angle in half. The three angle bisectors intersect in a single point, the incenter, which is the center of the triangle's incircle. The incircle is the circle that lies inside the triangle and touches all three sides. Its radius is called the inradius.

  6. Constructions in hyperbolic geometry - Wikipedia

    en.wikipedia.org/wiki/Constructions_in...

    Constructions in hyperbolic geometry. Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate, is changed. The fifth axiom of hyperbolic geometry says that given a line L and a point P not on that line, there are at least two lines passing through P ...

  7. Mass point geometry - Wikipedia

    en.wikipedia.org/wiki/Mass_point_geometry

    Mass point geometry, colloquially known as mass points, is a problem-solving technique in geometry which applies the physical principle of the center of mass to geometry problems involving triangles and intersecting cevians. [1] All problems that can be solved using mass point geometry can also be solved using either similar triangles, vectors ...

  8. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    Incircle and excircles. Incircle and excircles of a triangle. In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. [1] An excircle or escribed circle[2 ...

  9. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. [ 1 ] Angles formed by two rays are also known as plane angles as they lie in the plane that contains the rays. Angles are also formed by the intersection of two planes; these are called ...

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