Los Angeles Math Circle

11/11: Circle meeting (Dimitri Shlyakhtenko)

Geometry in three dimensions.
The focus of the circle meeting will be on three-dimensional objects, such as cubes, pyramids, prisms and so on.

Before coming to the circle meeting, try to solve the following problem. Draw a tetrahedron ABCD with A the top vertex and B,C,D the three bottom vertices. Pick a point each on the line segments AB, AC and CD. Let us call these points X, Y and Z. The plane through X, Y, Z intersects the tetrahedron in some way. Can you find the lines formed by the intersections of the faces of the tetrahedron with that plane?