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cot A+ cot B +cot C= R (a^2+b^2+c^2)/abc

Source: 2007 Swedish Mathematical Competition p3

April 27, 2021
trigonometrygeometrycircumradius

Problem Statement

Let α\alpha, β\beta, γ\gamma be the angles of a triangle. If aa, bb, cc are the side length of the triangle and RR is the circumradius, show that cot⁡α+cot⁡β+cot⁡γ=R(a2+b2+c2)abc \cot \alpha + \cot \beta +\cot \gamma =\frac{R\left(a^2+b^2+c^2\right)}{abc}
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