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Set Square

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?

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Biggest Bendy

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.

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Strange Rectangle

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.

Flexi Quad Tan

Stage: 5 Challenge Level: Challenge Level:1

Combine the result from the problem Flexi Quad Areas that the area $A(Q) = {\textstyle{1\over 2}}d_1d_2\sin\theta$ with the definition of the scalar product and use the result from the problem Flexi Quads that the scalar product of the diagonals is constant.
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