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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 ...
To construct the perpendicular bisector of the line segment between two points requires two circles, each centered on an endpoint and passing through the other endpoint (operation 2). The intersection points of these two circles (operation 4) are equidistant from the endpoints. The line through them (operation 1) is the perpendicular bisector.
O. Radko and E. Tsukerman, The Perpendicular Bisector Construction, the Isoptic Point and the Simson Line of a Quadrilateral, Forum Geometricorum 12: 161–189 (2012). External links [ edit ]
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 three perpendicular bisectors meet at the circumcenter. Other sets of lines associated with a triangle are concurrent as well. For example: Any median (which is necessarily a bisector of the triangle's area) is concurrent with two other area bisectors each of which is parallel to a side. [1]
The set of points equidistant from two points is a perpendicular bisector to the line segment connecting the two points. [8] The set of points equidistant from two intersecting lines is the union of their two angle bisectors. All conic sections are loci: [9] Circle: the set of points at constant distance (the radius) from a fixed point (the ...
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.
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