A triangle with a 45° angle is placed inside a square as shown. What’s the area proportion of parts A and B?
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The tip of the iceberg
Category: Advanced
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The Post-it note
Two unit squares (having side 1) are placed as shown. What is the total perimeter of the two red triangles?
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The wheelbarrow
A circle and two semicircles are nested as shown. What’s the proportion of their respective radii a : b : c ?
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The party hat
A cone has height 6 and base diameter 6. On it lie two points, one exactly halfway up, the other diametrically opposed at the base. What’s the shortest distance between these points going along the cone surface?
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The lazy spider
A spider situated at point A on the outside of a cylinder with diameter 4 and height 3 is trying to get to a fly at point C on the complete opposite side as fast as possible. What is the shortest route?
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The shark fin
An isosceles triangle is inscribed in a semicircle with one side along the diagonal and the top vertex somewhere on the semicircle. What’s the maximum fraction shaded?
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The snowman mansion
A square and a half square are stacked in order to form a house-shaped quadrilateral. Inside two circles are closely packed. What’s the angle between the tangency points?