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To generate the line that bisects the angle between two given rays [clarification needed] requires a circle of arbitrary radius centered on the intersection point P of the two lines (2). The intersection points of this circle with the two given lines (5) are T1 and T2. Two circles of the same radius, centered on T1 and T2, intersect at points P ...
Figure 9: The two tangent lines of the two tangent points of a given circle intersect on the radical axis R (red line) of the two solution circles (pink). The three points of intersection on R are the poles of the lines connecting the blue tangent points in each given circle (black).
The line connecting these common intersection points is the radical axis for all three circles. The two isodynamic points are inverses of each other relative to the circumcircle of the triangle. The centers of these three circles fall on a single line (the Lemoine line). This line is perpendicular to the radical axis, which is the line ...
This special line is the radical line of the two circles. Intersection of two circles with centers on the x-axis, their radical line is dark red. Special case = = = : In this case the origin is the center of the first circle and the second center lies on the x-axis (s. diagram).
Topological geometry deals with incidence structures consisting of a point set and a family of subsets of called lines or circles etc. such that both and carry a topology and all geometric operations like joining points by a line or intersecting lines are continuous.
Tangent lines to circles – Line which touches a circle at exactly one point; Versor – Quaternion of norm 1 (unit quaternion) Specific circles. Apollonian circles – Circles in two perpendicular families; Circles of Apollonius – Several sets of circles associated with Apollonius of Perga
The Apollonian circles are defined in two different ways by a line segment denoted CD. Each circle in the first family (the blue circles in the figure) is associated with a positive real number r , and is defined as the locus of points X such that the ratio of distances from X to C and to D equals r , { X | d ( X , C ) d ( X , D ) = r ...
In plane geometry, a lune (from Latin luna 'moon') is the concave-convex region bounded by two circular arcs. [1] It has one boundary portion for which the connecting segment of any two nearby points moves outside the region and another boundary portion for which the connecting segment of any two nearby points lies entirely inside the region.