Two smaller circles, centres $B$ and $C$ touch each other externally and touch the circle centre $A$ internally.
What happens to the perimeter of triangle $ABC$ as the two smaller circles roll around touching the inside rim of the bigger circle or as the two smaller circles vary in size?
Move the sliders to change the radii of the smaller circles and drag the point $B$ to move the circles.
Created with GeoGebra
You might like to download your own free copy of GeoGebra from the link above and draw this dynamic diagram for yourself. You will find it easy to get started on GeoGebra with the Quickstart guide for beginners.