Geometry Problem 1570: Calculating BE in Overlapping Squares: A High School and College Geometry Challenge

The squares ABCD and AEFG share a common vertex at A. If CF measures 6, calculate BE.

Diagram of Diagram of overlapping squares ABCD and AEFG with a common vertex at A. Geometry Problem 1570.

Two squares intertwine,
Vertex A unites their forms,
Geometry's quest.

Key Definitions and Descriptions

Key Term	Description
Overlapping Squares	Two squares that share a common vertex or side, creating a geometric intersection.
Vertex	A point where two or more lines or edges meet. In this problem, vertex A is common to both squares.
ABCD	One of the squares in the problem with vertices labeled A, B, C, and D.
AEFG	The other square in the problem with vertices labeled A, E, F, and G.
CF	The length of the side connecting vertices C and F, given as 6 units in this problem.
BE	The length of the side connecting vertices B and E, which needs to be calculated.