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Show that, for any values of $x$ and $y$ where $x> y$,
A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?
Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.