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  2. Midpoint - Wikipedia

    en.wikipedia.org/wiki/Midpoint

    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 ...

  3. Chord (geometry) - Wikipedia

    en.wikipedia.org/wiki/Chord_(geometry)

    A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow").

  4. Simson line - Wikipedia

    en.wikipedia.org/wiki/Simson_line

    The Simson line LN (red) of the triangle ABC with respect to point P on the circumcircle. In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. [1] The line through these points is the Simson line of P, named for Robert Simson. [2]

  5. Nine-point circle - Wikipedia

    en.wikipedia.org/wiki/Nine-point_circle

    [6]: p.153 Figure 3. A nine-point circle bisects a line segment going from the corresponding triangle's orthocenter to any point on its circumcircle. Figure 4. The center N of the nine-point circle bisects a segment from the orthocenter H to the circumcenter O (making the orthocenter a center of dilation to both circles): [6]: p.152

  6. Bisection - Wikipedia

    en.wikipedia.org/wiki/Bisection

    Line DE bisects line AB at D, line EF is a perpendicular bisector of segment AD at C, and line EF is the interior bisector of right angle AED. In geometry, bisection is the division of something into two equal or congruent parts (having the same shape and size). Usually it involves a bisecting line, also called a bisector.

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  9. Pedal circle - Wikipedia

    en.wikipedia.org/wiki/Pedal_circle

    Moreover, the midpoint of the line segment is the center of that pedal circle. [1] Griffiths' theorem states that all the pedal circles for a points located on a line through the center of the triangle's circumcircle share a common (fixed) point. [4] Consider four points with no three of them being on a common line.