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.
In a right-angled tetrahedron prove that the sum of the squares of
the areas of the 3 faces in mutually perpendicular planes equals
the square of the area of the sloping face. A generalisation of
Find the sides of an equilateral triangle ABC where a trapezium
BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are
2 possible interpretations.
Find lengths in terms of the radii of the two red semicircles.