Found problems: 3
Brazil L2 Finals (OBM) - geometry, 1998.2
Let $ABC$ be a triangle. $D$ is the midpoint of $AB$, $E$ is a point on the side $BC$ such that $BE = 2 EC$ and $\angle ADC = \angle BAE$. Find $\angle BAC$.
1998 Brazil National Olympiad, 2
Let $ABC$ be a triangle. $D$ is the midpoint of $AB$, $E$ is a point on the side $BC$ such that $BE = 2 EC$ and $\angle ADC = \angle BAE$. Find $\angle BAC$.
2016 India Regional Mathematical Olympiad, 6
$ABC$ is an equilateral triangle with side length $11$ units. Consider the points $P_1,P_2, \dots, P_10$ dividing segment $BC$ into $11$ parts of unit length. Similarly, define $Q_1, Q_2, \dots, Q_10$ for the side $CA$ and $R_1,R_2,\dots, R_10$ for the side $AB$. Find the number of triples $(i,j,k)$ with $i,j,k \in \{1,2,\dots,10\}$ such that the centroids of triangles $ABC$ and $P_iQ_jR_k$ coincide.