Pythagoras' theorem
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problemSix Discs
Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases? -
problemTwo Circles
Draw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap?
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problemBall Packing
If a ball is rolled into the corner of a room how far is its centre from the corner?
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problemThe Pillar of Chios
Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.
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problemCrescents and Triangles
Can you find a relationship between the area of the crescents and the area of the triangle?
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problemSqu-Areas
Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more triangular areas are enclosed. What is the area of this convex hexagon?
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problemCommon Tangent
Two circles touch, what is the length of the line that is a tangent to both circles?
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problemInterior Squares
Calculate the ratio of areas of these squares which are inscribed inside a semi-circle and a circle.