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No tangent line can be drawn through a point within a circle, since any such line must be a secant line. However, two tangent lines can be drawn to a circle from a point P outside of the circle. The geometrical figure of a circle and both tangent lines likewise has a reflection symmetry about the radial axis joining P to the center point O of ...
Tangent lines to circles; Circle packing theorem, the result that every planar graph may be realized by a system of tangent circles; Hexafoil, the shape formed by a ring of six tangent circles; Feuerbach's theorem on the tangency of the nine-point circle of a triangle with its incircle and excircles; Descartes' theorem; Ford circle; Bankoff circle
All tangent circles to the given circles can be found by varying line . Positions of the centers Circles tangent to two circles. If is the center and the radius of the circle, that is tangent to the given circles at the points ,, then:
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.
A circle is tangent to a point if it passes through the point, and tangent to a line if they intersect at a single point P or if the line is perpendicular to a radius drawn from the circle's center to P. Circles tangent to two given points must lie on the perpendicular bisector. Circles tangent to two given lines must lie on the angle bisector.
For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the extended Euclidean plane. Monge's theorem states that the three such points given by the three pairs of ...
Ford circle – Rational circle tangent to the real line; Fuhrmann circle; Generalised circle – Concept in geometry including line and circle; GEOS circle – Intersection of four lines associated with a generalized triangle; Great circle – Spherical geometry analog of a straight line Great-circle distance – Shortest distance between two ...
An osculating curve from a given family of curves is a curve that has the highest possible order of contact with a given curve at a given point; for instance a tangent line is an osculating curve from the family of lines, and has first-order contact with the given curve; an osculating circle is an osculating curve from the family of circles ...
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