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
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?
This is delightfully simple once you spot the way to do it, a real 'aha' question!