P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
A point P is selected anywhere inside an equilateral triangle. What
can you say about the sum of the perpendicular distances from P to
the sides of the triangle? Can you prove your conjecture?
Show that for any triangle it is always possible to construct 3
touching circles with centres at the vertices. Is it possible to
construct touching circles centred at the vertices of any polygon?
This interactivity is designed for the problem Cushion
The interactive diagram below has two labelled points, A and B.
What is the shortest path from A to B if you bounce off one
cushion? In the diagram, you can click on the "Show" buttons to
draw the four possible paths from A to B. Which is the shortest?
You may move A and B around by clicking on them.
What is the shortest path from A to B using exactly two
cushions? The interactive diagram below shows the eight possible
paths from A to B. How would you calculate the shortest path?