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  2. 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.

  3. Perpendicular - Wikipedia

    en.wikipedia.org/wiki/Perpendicular

    To make the perpendicular to the line AB through the point P using compass-and-straightedge construction, proceed as follows (see figure left): Step 1 (red): construct a circle with center at P to create points A' and B' on the line AB, which are equidistant from P. Step 2 (green): construct circles centered at A' and B' having equal radius.

  4. Concurrent lines - Wikipedia

    en.wikipedia.org/wiki/Concurrent_lines

    The perpendicular bisectors of all chords of a circle are concurrent at the center of the circle. The lines perpendicular to the tangents to a circle at the points of tangency are concurrent at the center. All area bisectors and perimeter bisectors of a circle are diameters, and they are concurrent at the circle's center.

  5. Thales's theorem - Wikipedia

    en.wikipedia.org/wiki/Thales's_theorem

    The locus of points equidistant from two given points is a straight line that is called the perpendicular bisector of the line segment connecting the points. The perpendicular bisectors of any two sides of a triangle intersect in exactly one point. This point must be equidistant from the vertices of the triangle.)

  6. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    Constructing the perpendicular bisector from a segment; Finding the midpoint of a segment. Drawing a perpendicular line from a point to a line. Bisecting an angle; Mirroring a point in a line; Constructing a line through a point tangent to a circle; Constructing a circle through 3 noncollinear points; Drawing a line through a given point ...

  7. Line (geometry) - Wikipedia

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

    Here, p is the (positive) length of the line segment perpendicular to the line and delimited by the origin and the line, and is the (oriented) angle from the x-axis to this segment. It may be useful to express the equation in terms of the angle α = φ + π / 2 {\displaystyle \alpha =\varphi +\pi /2} between the x -axis and the line.

  8. List of triangle inequalities - Wikipedia

    en.wikipedia.org/wiki/List_of_triangle_inequalities

    the perpendicular bisectors p a, p b, and p c of the sides (each being the length of a segment perpendicular to one side at its midpoint and reaching to one of the other sides); the lengths of line segments with an endpoint at an arbitrary point P in the plane (for example, the length of the segment from P to vertex A is denoted PA or AP);

  9. Equidistant - Wikipedia

    en.wikipedia.org/wiki/Equidistant

    Perpendicular bisector of a line segment. The point where the red line crosses the black line segment is equidistant from the two end points of the black line segment. The cyclic polygon P is circumscribed by the circle C. The circumcentre O is equidistant to each point on the circle, and a fortiori to each vertex of the polygon.