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unexpected properties
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Another property
A triangle is inscribed inside a circle, and then a circle is inscribed within that triangle. What property does the diagram have?

Look at the measurements here.
R²-2Rr=d², where R and r are the radii of the large and small circles respectively and d is the distance between their centres.

Finally, this diagram shows that there is an infinite number of triangles that have these two circles as inscribed and circumscribed circles. Move point X. Use the animation spring button animation spring to animate point X or one of the vertices of the first triangle.