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Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

Triangle Incircle Iteration

Keep constructing triangles in the incircle of the previous triangle. What happens?


Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?

Circle Scaling

Age 14 to 16 Challenge Level:

If the areas are in the ratio 1:2:3 what can you say about the ratio of the radii?

Can you find some key right-angled triangles that will give you the lengths you are after? Pythagoras' theorem is useful!

Some useful constructions can be found in the Thesaurus if you look up "construction". A perpendicular line might be particularly useful.