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The interior perpendicular bisector of a side of a triangle is the segment, falling entirely on and inside the triangle, of the line that perpendicularly bisects that side. The three perpendicular bisectors of a triangle's three sides intersect at the circumcenter (the center of the circle through the three vertices). Thus any line through a ...
In an axiomatic treatment of geometry, the notion of betweenness is either assumed to satisfy a certain number of axioms, or defined in terms of an isometry of a line (used as a coordinate system). Segments play an important role in other theories. For example, in a convex set, the segment that joins any two points of the set is contained in ...
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.
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 );
In geometry, the perpendicular bisector construction of a quadrilateral is a construction which produces a new quadrilateral from a given quadrilateral using the ...
The internal angle bisectors of a convex quadrilateral either form a cyclic quadrilateral [24]: p.127 (that is, the four intersection points of adjacent angle bisectors are concyclic) or they are concurrent. In the latter case the quadrilateral is a tangential quadrilateral.
Perpendicular bisector construction of a quadrilateral, on the use of perpendicular bisectors of a quadrilateral's sides to form another quadrilateral Topics referred to by the same term This disambiguation page lists articles associated with the title Perpendicular bisector construction .
The tangent line through a point P on the circle is perpendicular to the diameter passing through P. If P = (x 1, y 1) and the circle has centre (a, b) and radius r, then the tangent line is perpendicular to the line from (a, b) to (x 1, y 1), so it has the form (x 1 − a)x + (y 1 – b)y = c.