Difference between revisions of "2005 IMO Problems/Problem 1"
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Six points are chosen on the sides of an equilateral triangle <math>ABC</math>: <math>A_1, A_2</math> on <math>BC</math>, <math>B_1</math>, <math>B_2</math> on <math>CA</math> and <math>C_1</math>, <math>C_2</math> on <math>AB</math>, such that they are the vertices of a convex hexagon <math>A_1A_2B_1B_2C_1C_2</math> with equal side lengths. Prove that the lines <math>A_1B_2, B_1C_2</math> and <math>C_1A_2</math> are concurrent. | Six points are chosen on the sides of an equilateral triangle <math>ABC</math>: <math>A_1, A_2</math> on <math>BC</math>, <math>B_1</math>, <math>B_2</math> on <math>CA</math> and <math>C_1</math>, <math>C_2</math> on <math>AB</math>, such that they are the vertices of a convex hexagon <math>A_1A_2B_1B_2C_1C_2</math> with equal side lengths. Prove that the lines <math>A_1B_2, B_1C_2</math> and <math>C_1A_2</math> are concurrent. | ||
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| + | ==Solution== | ||
| + | {{solution}} | ||
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| + | ==See Also== | ||
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| + | {{IMO box|year=2005|before=First Problem|num-a=2}} | ||
Latest revision as of 23:56, 18 November 2023
Problem
Six points are chosen on the sides of an equilateral triangle 
: 
on 
, 
, 
on 
and 
, 
on 
, such that they are the vertices of a convex hexagon 
with equal side lengths. Prove that the lines 
and 
are concurrent.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 2005 IMO (Problems) • Resources | ||
| Preceded by First Problem |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
| All IMO Problems and Solutions | ||
