problem

### Calculating with cosines

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

problem
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Calculating with cosines

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

problem
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Cubestick

Stick some cubes together to make a cuboid. Find two of the angles
by as many different methods as you can devise.

problem
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Cyclic Triangles

Make and prove a conjecture about the cyclic quadrilateral
inscribed in a circle of radius r that has the maximum perimeter and the maximum area.

problem
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Xtra

Find the sides of an equilateral triangle ABC where a trapezium
BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are
2 possible interpretations.

problem
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Three by One

There are many different methods to solve this geometrical problem - how many can you find?

problem
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Hexy-Metry

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

problem
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Pythagoras for a Tetrahedron

In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation of Pythagoras' Theorem.

problem
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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.