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Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?

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Square World

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?

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30-60-90 Polypuzzle

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

Just Touching

Age 16 to 18 Challenge Level:

Two semi-circles are drawn on one side of a line segment. Another semi-circle touches them externally as shown in the diagram.

What is the radius of the circle that touches all three semi-circles?