MathDB

2

Part of 1984 Czech And Slovak Olympiad IIIA

Problems(1)

cosA+cosB+cosC+cosD =0 => ABCD is cyclic or trapezoid

Source: Czech and Slovak Olympiad 1984, National Round, Problem 2

9/11/2024
Let α,β,γ,δ\alpha, \beta, \gamma, \delta be the interior angles of a convex quadrilateral, If cos⁡α+cos⁡β+cos⁡γ,+cos⁡δ=0, \cos\alpha + \cos\beta + \cos\gamma, + \cos\delta = 0 , then this quadrilateral is cyclic or a trapezium. Prove it.
geometrytrigonometrytrapezoid