You may also like

Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?


A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

Half a Triangle

Age 14 to 16
Challenge Level

This problem will need solving in stages by most students.

Perhaps beginning by establishing the required line ratio.

Then by remembering a familiar figure where that particular ratio can be found.

Deciding how that figure can be constructed on the given triangle to locate a useful point.

Finally creating the required line, parallel to the base, across the triangle.