Difference between revisions of "1992 OIM Problems/Problem 6"
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== Problem == | == Problem == | ||
From the triangle <math>T</math> with vertices <math>A</math>, <math>B</math> and <math>C</math>, the hexagon <math>H</math> with vertices <math>A_1</math>, <math>A_2</math>, <math>B_1</math>, <math>B_2</math>, <math>C_1</math>, <math>C_2</math> is constructed as shown in the figure. | From the triangle <math>T</math> with vertices <math>A</math>, <math>B</math> and <math>C</math>, the hexagon <math>H</math> with vertices <math>A_1</math>, <math>A_2</math>, <math>B_1</math>, <math>B_2</math>, <math>C_1</math>, <math>C_2</math> is constructed as shown in the figure. | ||
| − | |||
| − | |||
Show that: | Show that: | ||
<cmath>area(H) \ge 13.area(T)</cmath> | <cmath>area(H) \ge 13.area(T)</cmath> | ||
| + | |||
| + | [[File:ibe7_2.gif|center]] | ||
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Revision as of 14:08, 13 December 2023
Problem
From the triangle 
with vertices 
, 
and 
, the hexagon 
with vertices 
, 
, 
, 
, 
, 
is constructed as shown in the figure.
Show that:
![\[area(H) \ge 13.area(T)\]](http://latex.artofproblemsolving.com/f/c/4/fc4e404f0e7cc3851c1dfea4d938a092dbdf78e5.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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