Compare Areas
Age 14 to 16
Challenge Level 
Which lengths are equal in the diagrams?
Which angles are equal?
Let AB = BC = 12cm
Have a go at drawing each diagram.
Of the two squares, which has the greatest area?
How do you know?
Draw the radii at the points where the circle touches the triangle.
If the radius of the circle is r, can you find the hypotenuse of the triangle in terms of r?
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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?
Medallions
Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?