ArchimedesTwinCircles

Archimedes proved that the purple circle, tangent to the enclosing circle, the red circle and the perpendicular dividing line, is congruent to the green circle tangent to the enclosing circle, the blue circle and the dividing line. The trace checkbox shows a tracing point I used to help figure out that the centers of the twin circle should be on parabolas. (If you turn the point on, try to move it while keeping two of the distances equal.) The parabolas checkbox shows the parabolas that intersect to find the centers of the twin circles. They were defined using GeoGebra's parabola tool that has input of the focus and the directrix. I first saw the theorem at the Futility Closet, [url]http://www.futilitycloset.com/2014/03/20/archimedes-twin-circles/[/url] My think aloud about making this is on my blog, [url]http://mathhombre.blogspot.com/2014/03/archimedes-twin-circles.html[/url]

 

John Golden

 
Resource Type
Activity
Tags
archimedes  circle  closet  directrix  futility  parabola  tangent 
Target Group (Age)
15 – 18
Language
English
 
 
GeoGebra version
4.4
Views
3188
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License
CC-BY-SA, GeoGebra Terms of Use
Derived Resources
ArchimedesTwinCircles
Shared by xlenchik
 
 
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