Orthogonal circles

Short description: Circles whose tangent lines at the points of intersection are perpendicular

Three mutually orthogonal circles

In geometry, two circles are said to be orthogonal if their respective tangent lines at the points of intersection are perpendicular (meet at a right angle).

A straight line through a circle's center is orthogonal to it, and if straight lines are also considered as a kind of generalized circles, for instance in inversive geometry, then an orthogonal pair of lines or line and circle are orthogonal generalized circles.

In the conformal disk model of the hyperbolic plane, every geodesic is an arc of a generalized circle orthogonal to the circle of ideal points bounding the disk.

See also

• Radical axis
• Power center (geometry)
• Apollonian circles
• Bipolar coordinates

References

• Chaplick, Steven; Förster, Henry; Kryven, Myroslav; Wolff, Alexander (2019). "Graph Drawing and Network Visualization, Proceedings of the 27th International Symposium". in Archambault, D.; Tóth, C.. GD 2019, Prague, Czech Republic, September 17–20, 2019. Springer. pp. 216–229. doi:10.1007/978-3-030-35802-0_17. 
• Court, Nathan Altshiller (1952), "8.B. Orthogonal Circles", College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (2nd ed.), Barnes & Noble, §§ 263–272, Template:Pgs, https://archive.org/details/collegegeometryi00newy/page/174/ 
• Coxeter, H. S. M.; Greitzer, S. L. (1967), Geometry Revisited, MAA, p. 115 
• Fraivert, David; Stupel, Moshe (2022), "Necessary and sufficient conditions for orthogonal circles", International Journal of Mathematical Education in Science and Technology 53 (10): 2837–2848, doi:10.1080/0020739X.2021.1945153