Question 83
We are given an equilateral triangle $ABC$ with sides of length $2$. We consider all equilateral triangles $PQR$ with sides of length $1$ satisfying the following properties:
* $P$ lies on the side $AB$,
* $Q$ lies on the side $AC$ and
* $R$ lies in the interior or on the edge of the triangle $ABC$,
Describe the set of all points in the triangle $ABC$ that are centroids of such triangles $PQR$.
* $P$ lies on the side $AB$,
* $Q$ lies on the side $AC$ and
* $R$ lies in the interior or on the edge of the triangle $ABC$,
Describe the set of all points in the triangle $ABC$ that are centroids of such triangles $PQR$.