2023 OIM Problems/Problem 4

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Problem

Let $B$ and $C$ be two fixed points in the plane. For each point $A$, outside of the line $BC$, let $G$ be the centroid of the triangle $ABC$. Find the locus of points $A$ such that $\angle BAC + \angle BGC = 180^{\circ}$.

Note: The locus is the set of points in the plane satisfying the property.

Solution

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See also

https://sites.google.com/associacaodaobm.org/oim-brasil-2023/pruebas