Two circles with centers at (x_i, y_i) with radii r_i for i = 1, 2 are mutually tangent if (x_1 - x_2)^2 + (y_1 - y_2)^2 = (r_1 ± r_2)^2. If the center of the second circle is inside the first, then the - and + signs both correspond to internally tangent circles. If the center of the second circle is outside the first, then the - sign corresponds to externally tangent circles and the + sign to internally tangent circles. Finding the circles tangent to three given circles is known as Apollonius' problem. The Desborough Mirror, a beautiful bronze mirror made during the Iron Age between 50 BC and 50 AD, consists of arcs of circles that are exactly tangent.
Apollonius' problem | Casey's theorem | chain of circles | circle-circle tangents | circle packing | Descartes circle theorem | excircles | four coins problem | Hawaiian earring | incircle | inner Soddy circle | lens | lune | Malfatti circles | Malfatti's problem | nine circles theorem | outer Soddy circle | oval | Pappus chain | seven circles theorem | six circles theorem | Soddy circles | tangent curves | tangent spheres
We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.
Club Z! has connected me with a tutor through their online platform! This was exactly the one-on-one attention I needed for my math exam. I was very pleased with the sessions and ClubZ’s online tutoring interface.
My son was suffering from low confidence in his educational abilities. I was in need of help and quick. Club Z! assigned Charlotte (our tutor) and we love her! My son’s grades went from D’s to A’s and B’s.
I’ve been using Club Z’s online classrooms to receive some help and tutoring for 2 of my college classes. I must say that I am very impressed by the functionality and ease of use of their online App. Working online with my tutor has been a piece of cake. Thanks Z.
Jonathan is doing really well in all of his classes this semester, 5 A’s & 2 B’s (he has a computer essentials class instead of PLC). In his Algebra class that Nathan is helping him with he has an A+.
Sarah is very positive, enthusiastic and encourages my daughter to do better each time she comes. My daughter’s grade has improved, we are very grateful for Sarah and that she is tutoring our daughter. Way to go ClubZ!
