MathDB

The base of a regular quadrilateral pyramid

\pi

is a square with side length

2a

and its lateral edge has length a

\sqrt{17}

. Let

M

be a point inside the pyramid. Consider the five pyramids which are similar to

\pi

, whose top vertex is at

M

and whose bases lie in the planes of the faces of

\pi

. Show that the sum of the surface areas of these five pyramids is greater or equal to one fifth the surface of

\pi

, and find for which

M

equality holds.

Problem Statement