Problem A. 678. (October 2016)

A. 678. The convex polyhedron $\displaystyle \mathcal{K}$ has five vertices, $\displaystyle A$, $\displaystyle B$, $\displaystyle C$, $\displaystyle D$ and $\displaystyle E$. The line segment $\displaystyle DE$ intersects the plane of the triangle $\displaystyle ABC$ in the interior of the triangle. Show that $\displaystyle \mathcal{K}$ has an inscribed sphere – with being tangent to all six faces – if and only if the inscribed spheres of the terahedra $\displaystyle ABCD$ and $\displaystyle ABCE$ are tangent to each other.

(5 pont)

Deadline expired on November 10, 2016.

Statistics:

6 students sent a solution.
5 points:	Baran Zsuzsanna, Bukva Balázs, Williams Kada.
4 points:	Lajkó Kálmán.
2 points:	1 student.
1 point:	1 student.

Problems in Mathematics of KöMaL, October 2016