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Flexi Quads

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

Flexi Quad Tan

As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.

Air Routes

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Bond Angles

Age 16 to 18
Challenge Level
Try drawing the tetrahedral molecule with some axes on it and use simple trigonometry to define the coordinates of each of the outer atoms. It may be useful to let one of the bottom atoms to lie along an axis. To find the coordinates of the other two bottom atoms, it is easiest to draw a top-down diagram to help...