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

NOTES AND BACKGROUND

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