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Just Touching

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?

Square World

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

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.

Biggest Bendy

Age 16 to 18 Challenge Level:

You may wish to try the problem Bendy Quad first.

 

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.