You may also like

problem icon

Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

problem icon

Grid Points on Hyperbolas

Find a condition which determines whether the hyperbola y^2 - x^2 = k contains any points with integer coordinates.

problem icon

Parabella

This is a beautiful result involving a parabola and parallels.

Napoleon's Hat

Stage: 5 Challenge Level: Challenge Level:1

hat
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?

Created with GeoGebra


You can download your own free copy of Geogebra from the above link and draw your own dynamic diagrams.