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ABC is right triangled iff cyc sum sin A=1+cyc sum cos A

Source: Vietnam MO 1981 P1

March 17, 2011
trigonometrygeometryperimetercircumcircleinradiusgeometry unsolved

Problem Statement

Prove that a triangle ABCABC is right-angled if and only if sin⁡A+sin⁡B+sin⁡C=cos⁡A+cos⁡B+cos⁡C+1\sin A + \sin B + \sin C = \cos A + \cos B + \cos C + 1
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