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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?

Compare Areas

Age 14 to 16
Challenge Level

Compare Areas printable sheet

ABC is an isosceles right angled triangle.
Each diagram has a different shape inscribed within it.

Which of the inscribed figures has the greatest area?

Click here for a poster of this problem.