Stage: 5 Challenge Level: 
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The diagram shows three equilateral triangles $ABC,
AYX$ and $XZB$. The point $X$ is a moveable point on
$AB$. The points $P$, $Q$ and $R$ are the centres of
the three triangles.
Experiment with the dynamic diagram.
What can you say about triangle $PQR$?
Can you prove your conjecture?
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Created with GeoGebra |
You can download your own free copy of Geogebra from the above link and draw your own dynamic diagrams.
Interactivities. Dividing line in given ratio. Coordinates. Dynamic geometry. Number theory. Calculating with ratio & proportion. Mathematical reasoning & proof. Centroid. Inequality/inequalities. Manipulating algebraic expressions/formulae.
Published April 2000.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk
