3

Part of 2003 Czech-Polish-Slovak Match

Problems(1)

a,b,c and pa,qb,rc triangles with equal areas

Source: Czech-Polish-Slovak Match 2003

p,q,r

lies in the interval

(\frac{2}{5},\frac{5}{2})

pqr=1

. Prove that there exist two triangles of the same area, one with the sides

a,b,c

and the other with the sides

pa,qb,rc

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