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

A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Grid Lockout

Age 14 to 16 Challenge Level:

Investigate the areas of squares formed by joining points on a
square grid and show that it is impossible to construct any square
whose area is (4n + 3) where n is an integer.