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As x and y change the points S, P, Q and R always lie on the circle with SQ as diameter and the angles of the quadrilateral SPQR remain the same. (See the problem Strange Rectangle from November 2001.)
Taking
x = \sqrt{3} and y = 1
find all the angles in this figure and the exact values of the sine, cosine and tangent of these angles in surd form.Now take
x = \sqrt{2} + 1 and y = 1
and find the exact values of the trigonometric ratios for 22.5^o and 67.5^oA 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?
ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.