Two Squares and Another Square

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Two Squares and Another Square: What is that about?
A Mathematical Droodle

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Copyright © 1996-2012 Alexander Bogomolny

Explanation

The applet suggests the following statment:

(1) Given two squares ABCD and A'B'C'D' and a point P, let A₁ = P + AA', B₁ = P + BB', C₁ = P + CC', and D₁ = P + DD'. Then A₁B₁C₁D₁ is a square.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

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What if applet does not run?

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 © 1996-2012 Alexander Bogomolny

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