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 Orthogonality Radical axis Power center (geometry) Apollonian circles Bipolar coordinates
References Chaplick, Steven; Förster, Henry; Kryven, Myroslav; Wolff, Alexander (2019), "On arrangements of orthogonal circles", in Archambault, D.; Tóth, C. (eds.), Graph Drawing and Network Visualization, Proceedings of the 27th International Symposium, GD 2019, Prague, Czech Republic, September 17–20, 2019, Springer, pp. 216–229, arXiv:1907.08121, doi:10.1007/978-3-030-35802-0_17 Court, Nathan Altshiller (1952) [1st ed. 1925], "8.B. Orthogonal Circles", College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (2nd ed.), Barnes & Noble, §§ 263–272, pp. 174–177 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