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Geometry Problem 1319: Hexagons, Equilateral Triangles, Centers, Midpoints. Level: School, College, Mathematics Education

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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.
 
 

Geometry Problem 1319: Hexagons, Equilateral Triangles, Center, Midpoints. Level: School, College, Mathematics Education
 

See also:
Sketch of problem 1319 using mobile apps

Home | Geometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | Problems Art Gallery | 1311-1320 | Triangle | Equilateral Triangle | Center | Hexagon | Midpoint | by Antonio Gutierrez

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