Three semi-circles have a common diameter, each touches the other
two and two lie inside the biggest one. What is the radius of the
circle that touches all three semi-circles?
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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Four rods are hinged at their ends to form a quadrilateral with
fixed side lengths. Show that the quadrilateral has a maximum area
when it is cyclic.