The figure shows a hexagon
A1A2A3A4A5A6
with equilateral triangles
A1A2B1,... A6A1B6.of
centers O1, O2, ..., O6. Q1, Q2, ...,Q6 are the centers of equilateral
triangles B1B2C1, ..., B6B1C6. O14, O25, O36, Q14, Q25, and Q36
are the midpoints of O1O4, O2O5, O3O6, Q1Q4, Q2Q5, and Q3Q6,
respectively. Prove that (1) Triangles O14O25O36 and Q14Q25Q36
are equilateral; (2) O14, O25, and O36 are the midpoints of
Q14Q36, Q14Q25, and Q25Q36, respectively.
See also:
Solution
by Ignacio Larrosa Caņestro
Geogebra: Dynamic illustration by Ignacio Larrosa Caņestro
Sketch of problem 1319 using mobile apps
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