Editing ApolloniusProblem
You are currently browsing as guest..
To change this, fill in the following fields:
Username
Password
Click here to reset your password
Who can read this page?
The World
Members
Council
Admin
You have been granted an edit lock on this page
until Sat Apr 27 01:29:03 2024.
Press
to finish editing.
Who can edit this page?
World editing disabled
Members
Council
Admin
Apollonius' Problem is to draw a circle which touches (is a tangent to) another 3 objects - either points (P), lines (L) or circles (C). The most general case is the circle which is a tangent to 3 other circles (CCC) when there are 8 solutions. IMG:problem.png The construction of these circles is not a trivial task. The method is given at: http://mathworld.wolfram.com/ApolloniusProblem.html and clarification can be found at: www.ajur.uni.edu/v3n1/Gisch and Ribando.pdf The case of the circle touching 3 points (PPP) is the classical circumcircle of a triangle and is a unique solution. There are 8 other cases PPL, CPL etc. which have differing numbers of solutions and complexity of construction. Construction of the solution to these problems is described at: http://en.wikipedia.org/wiki/Special_cases_of_Apollonius'_problem Most of the techniques required are hotlinked in these page however http://web.mat.bham.ac.uk/C.J.Sangwin/Teaching/geom/Tangent_circle_circle/ruler-compass/circle-circle-tangent-rulercompass.html describes carefully the necessary technique for forming the four tangents to two circles. The free online drawing package Geogebra makes the investigation of these problems an easier exercise.