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

Given circles 1, 2, 3 (with radii r₁, r₂, and r₃ respectively), and 3 squares packed in a right triangle, as shown, find the lenght of r₂.
Trois cercles 1, 2, 3 (avec respectivement des rayons r₁, r₂, et r₃), et 3 carrés sont empilés dans un triangle rectangle, comme illustré, trouver la longueur de r₂ !
Tre cerchi 1, 2, 3 (con rispettivi raggi r₁, r₂, r₃), e 3 quadrati sono confezionati in un triangolo rettangolo, come mostrato, trova la lunghezza di r₂.

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Solution: The three triangles that inscribe 1, 2 and 3 are similar to each other and the size of the triangles is increasing at the same rate. So, r3/r2 = r2/r1 which gives r2 = √(r1r3) Please spread the word about the Sunday Puzzle!