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IMO 1967 - Longlist Problems Question 39

IMO Shortlist · IMO 1967 - Longlist Problems

Question 39

(POL 4) Show that the triangle whose angles satisfy the equality
$$\frac{\sin^2A+\sin^2B+\sin^2C}{\cos^2A+\cos^2B+\cos^2C}=2$$
is a right-angled triangle.