APOLLONIUS PROBLEM A Problem From Euclidean Plane Geometry

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CAN YOU DRAW EIGHT CIRCLES TANGENT TO THREE GIVEN CIRCLES ? • In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane. Apollonius of Perga (c. 262 BC – c. 190 BC) posed and solved this famous problem in his work Ἐπαφαί (Epaphaí, Tangencies ); this work has been lost, but a 4th-century AD report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them, a pair of solutions for each way to divide the three given circles in two subsets (there are 4 ways to divide a set of cardinality 3 in 2 parts). • #Apollonius #Problem • Subscribe: BRAIN EXPLODERS • Link: / brainexploders • Watch the video and Learn Something Extraordinary... • 00:00 | Introduction • 00:16 | How many required circles can be constructed • 01:19 | General Statement of Apollonius Problem • 01:42 | What if all the circles are of infinite radius? • 02:01 | Some simple cases • 04:09 | How to find a reference circle such that inverse of 2 given circles in it, become concentric? • 04:28 | What is Radical Axis • 05:47 | Resizing • 06:33 | First Approach - Change the radii such that any two circles become tangent • 07:44 | Second Approach - Resizing the circles such that one of the circle becomes a point • 08:06 | With the help of inversive geometry, we can find the solutions in pairs. • 08:51 | How to draw orthogonal circle • Get early access and support the channel on Patreon • Link: / brainexploders • Suggested Book: • Title: Problems and Solutions in Euclidean Geometry (Dover Books on Mathematics) • Link: https://amzn.to/36ut8HZ • A challenge for you in the last of this videos of the playlist Exploders Contest, can you solve that questions? Watch the videos, Take your time give your answer in the comment section, if your answer is correct, we'll announce your name in our next YouTube video of this playlist - • Exploders Contest: Season 2 • Link: • EXPLODERS CONTEST: Season 2 • Exploders Contest: Season 1 • Link: • EXPLODERS CONTEST: Season 1 • This is the channel to feature this type of questions suggested by the people. • Join us on another platforms: • Instagram: @Brain_Exploders • Facebook: @BrainExploders • Twitter: @BrainExploders • Telegram: @Brain_Exploders • ___Show your support to us. • ________THANKS FOR WATCHING • #Brain_Exploders • _______________Next video will come soon.

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