- Source: 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
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
Kata Kunci Pencarian:
- Orthogonal circles
- Radical axis
- Tangent lines to circles
- Power of a point
- Zernike polynomials
- Circles of Apollonius
- Orthogonal trajectory
- Orthogonal polynomials on the unit circle
- Apollonian circles
- Orthogonal matrix
