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:
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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