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?

Four rods are hinged at their ends to form a convex quadrilateral.
Investigate the different shapes that the quadrilateral can take.
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Hexagon Perimeter

Age 14 to 16 Short Challenge Level

A circle of radius 1 is inscribed in a regular hexagon, as shown below. What is the perimeter of the hexagon?