Archimedes Laboratory Project™
Puzzles & Mental Activities that Enhance Critical and Creative Thinking Skills

	Visually prove that if 3 equal circles mutually intersect one another in an arbitrary point P, then the circle passing through their other three pairwise points of intersection (A, B, and C respectively) is congruent to the original 3 circles. Prouvez visuellement que si trois cercles égaux se coupent mutuellement en un seul point P quelconque, alors le cercle passant par leurs trois autres points d'intersection (A, B, et C, respectivement) est congruent à ces 3 cercles. Dimostra in modo visivo che se 3 cerchi uguali si intersecano reciprocamente in un sol punto arbitrario P, allora il cerchio che passa per i loro altri tre punti di intersezione (rispettivamente A, B e C) è congruente ai 3 cerchi originali. You can comment and discuss this puzzle on our FaceBook or Blogger web page. › Click to show/hide the solution Solution: If you connect the radii and the intersection points together you will obtain a 3D cubic wireframe with edges of equal length, as shown in the picture. The vertex Q of the cube is center of the circumcircle of ABC, therefore it is congruent to the other 3 circles. This problem is known as “Johnson circle theorem”. Please spread the word about the Sunday Puzzle!

Text and images by Gianni A. Sarcone 
Labels: SUNDAY PUZZLE, puzzles to solve, recreational mathematics, circumcircle
You can use the material shown on this page for educational purpose only as long as you credit us [© G. Sarcone, www.archimedes-lab.org] and link back to archimedes-lab.org
Sunday Puzzle by Gianni A. Sarcone is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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