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  2. Distance from a point to a line - Wikipedia

    en.wikipedia.org/.../Distance_from_a_point_to_a_line

    The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.

  3. Desargues's theorem - Wikipedia

    en.wikipedia.org/wiki/Desargues's_theorem

    Further, if the two triangles lie on different planes, then the point AB ∩ ab belongs to both planes. By a symmetric argument, the points AC ∩ ac and BC ∩ bc also exist and belong to the planes of both triangles. Since these two planes intersect in more than one point, their intersection is a line that contains all three points.

  4. Tangent lines to circles - Wikipedia

    en.wikipedia.org/wiki/Tangent_lines_to_circles

    No tangent line can be drawn through a point within a circle, since any such line must be a secant line. However, two tangent lines can be drawn to a circle from a point P outside of the circle. The geometrical figure of a circle and both tangent lines likewise has a reflection symmetry about the radial axis joining P to the center point O of ...

  5. Distance between two parallel lines - Wikipedia

    en.wikipedia.org/wiki/Distance_between_two...

    the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line y = − x / m . {\displaystyle y=-x/m\,.} This distance can be found by first solving the linear systems

  6. Euler line - Wikipedia

    en.wikipedia.org/wiki/Euler_line

    In geometry, the Euler line, named after Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər), is a line determined from any triangle that is not equilateral.It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.

  7. Five points determine a conic - Wikipedia

    en.wikipedia.org/wiki/Five_points_determine_a_conic

    In Euclidean and projective geometry, five points determine a conic (a degree-2 plane curve), just as two (distinct) points determine a line (a degree-1 plane curve). There are additional subtleties for conics that do not exist for lines, and thus the statement and its proof for conics are both more technical than for lines.

  8. Duality (projective geometry) - Wikipedia

    en.wikipedia.org/wiki/Duality_(projective_geometry)

    The line joining two self-conjugate points cannot be a self-conjugate line. A line cannot contain more than two self-conjugate points. A polarity induces an involution of conjugate points on any line that is not self-conjugate. A triangle in which each vertex is the pole of the opposite side is called a self-polar triangle.

  9. Line–line intersection - Wikipedia

    en.wikipedia.org/wiki/Lineline_intersection

    The intersection point above is for the infinitely long lines defined by the points, rather than the line segments between the points, and can produce an intersection point not contained in either of the two line segments. In order to find the position of the intersection in respect to the line segments, we can define lines L 1 and L 2 in terms ...

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