What is the area of the coloured figure? Can you determine the area without counting the number of squares in each different-coloured shape?
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Running man
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Baby steps
The edges of a cyclic quadrilateral extend to two intersections. O is the circle centre. The two diagonals intersect inside the circle. What is the angle α?
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The party hat II
An equilateral triangle with a circular arc through its red centre and two vertices. If the yellow area equals the green one, what’s the angle α?
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The lighthouse
A parallelogram and four equilateral triangles. What is yellow : green?
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Holes in my heart
The heart is divided into right triangles, each of which contains a blue circle. What is the total circumference of the blue circles in relation to the green perimeter and the lengths of the purple and orange lines in the centre?
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Tip of the veil
A square with two right angles. What fraction is yellow?
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The crosshairs
A regular pentagon and two semicircles. Prove that they are orthogonal, i.e. the tangents in the intersection point are orthogonal.
Some chords and segments inside a semicircle. What is the ratio of red to blue?
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Three times three
A regular nonagon and two equilateral triangles. What’s the angle α?
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The laser game
In an equilateral triangular mirror room a laser is shot from the top vertex down to the base. The light ray bounces three times to return to the same base point. What is the angle α?