MathDB
finite no of equal circles inside equilateral

Source: Chile Finals 2010 L2 p6

October 5, 2022
geometrycombinatoricscombinatorial geometry

Problem Statement

Prove that in the interior of an equilateral triangle with side aa you can put a finite number of equal circles that do not overlap, with radius r=a2010r = \frac{a}{2010}, so that the sum of their areas is greater than 17380\frac{17\sqrt3}{80} a2^2.