Romania NMO 2023 Grade 10 P3
Source: Romania National Olympiad 2023
April 14, 2023
geometrycomplex numbers
Problem Statement
We consider triangle and variables points on the half-line , on the half-line , and on the half-line , each start simultaneously from and respectively , moving with constant speeds , where , , and are expressed in the same unit of measure.a) Given that there exist three distinct moments in which triangle is equilateral, prove that triangle is equilateral and that .b) Prove that if and there exists a moment in which triangle is equilateral, then triangle is also equilateral.