1995 IMO Problems/Problem 3: Difference between revisions
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==Problem== | ==Problem== | ||
Determine all integers <math>n>3</math> for which there exist <math>n</math> points <math>A_1,\ldots,A_n</math> in the plane, no three collinear, and real numbers <math>r_1,\ldots,r_n</math> such that for <math>1\le i<j<k\le n</math>, the area of <math>\triangle A_iA_jA_k</math> is <math>r_i+r_j+r_k</math>. | Determine all integers <math>n>3</math> for which there exist <math>n</math> points <math>A_1,\ldots,A_n</math> in the plane, no three collinear, and real numbers <math>r_1,\ldots,r_n</math> such that for <math>1\le i<j<k\le n</math>, the area of <math>\triangle A_iA_jA_k</math> is <math>r_i+r_j+r_k</math>. | ||
==Solution== | |||
{{solution}} | |||
{{IMO box|year=1995|num-b=2|num-a=4}} | {{IMO box|year=1995|num-b=2|num-a=4}} | ||
Latest revision as of 20:39, 4 July 2024
Problem
Determine all integers 
for which there exist 
points 
in the plane, no three collinear, and real numbers 
such that for 
, the area of 
is 
.
Solution
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