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(acosA + bcosB + ccosC)/(asinA + bsinB + csinC) = (a + b + c)/9R

Source: Vietnamese MO (VMO) 1976 P2

August 20, 2018
geometrytrigonometrycircumradius

Problem Statement

Find all triangles ABCABC such that acosA+bcosB+ccosCasinA+bsinB+csinC=a+b+c9R\frac{a cos A + b cos B + c cos C}{a sin A + b sin B + c sin C} =\frac{a + b + c}{9R}, where, as usual, a,b,ca, b, c are the lengths of sides BC,CA,ABBC, CA, AB and RR is the circumradius.
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