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'Cyclic Triangles' printed from http://nrich.maths.org/
A triangle $ABC$ is inscribed in a circle with $AB$ as diameter.
Find the maximum value of $AC + CB$.
Now generalise your result to the case where $AB$ is fixed but not
a diameter of the circle.
Make and prove a conjecture about the cyclic quadrilateral
inscribed in a circle of radius $r$ that has the maximum perimeter
and the maximum area.
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