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PrintFall Mathematical Competition
Bulgaria geometry
Problem
Determine the locus of the points which are interior for the convex quadrilateral and the areas of the quadrilaterals and are equal.
Solution
The locus is the segment such that and , where and are the areas of triangles and , respectively.
Final answer
The locus is the segment PQ inside ABCD where PQ is parallel to AC and at perpendicular distance |S_ABC − S_ACD| / AC from AC, with S_ABC and S_ACD the areas of triangles ABC and ACD.
Techniques
Constructions and lociDistance chasing