# Two Squares and Another Square

What is that about?

A Mathematical Droodle

1 June 2015, Created with GeoGebra

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Copyright © 1996-2017 Alexander Bogomolny

### Explanation

The applet suggests the following statment:

Given two squares ABCD and A'B'C'D' and a point P, let A_{1} = P + AA', B_{1} = P + BB', C_{1} = P + CC', and D_{1} = P + DD'. Then A_{1}B_{1}C_{1}D_{1} is a square.

This is problem 46a from Yaglom. One solution follows from a more general statement about two directly similar figures.

### References

- I. M. Yaglom,
*Geometric Transformations II*, MAA, 1968

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Copyright © 1996-2017 Alexander Bogomolny

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