Geodesic
Inequalities Associated with the Triangle
Canadian mathematical bulletin, Tome 8 (1965) no. 5, pp. 615-626

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Let R, r, s represent respectively the circumradius, the inradius and the semiperimeter of a triangle with sides a, b, c. Let f(R, r) and F(R, r) be homogeneous real functions. Let q(R, r) and Q(R, r) be real quadratic forms. The latter functions are thus a special case of the former. Our main result is to derive the strongest possible inequalities of the form 1 with equality only for the equilateral triangle. 
Blundon, W. J. Inequalities Associated with the Triangle. Canadian mathematical bulletin, Tome 8 (1965) no. 5, pp. 615-626. doi: 10.4153/CMB-1965-044-9
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     title = {Inequalities {Associated} with the {Triangle}},
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     year = {1965},
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     doi = {10.4153/CMB-1965-044-9},
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