A triangle with a quadrilateral that covers half its area. What is the angle?
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The flying banner
Category: Advanced
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The PowerPoint
A point lies 8 from the centre of a circle of radius 6. The angle α is variable. What’s the maximum triangle area?
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Who’s afraid of red, yellow and blue?
Three squares. The top line segment is variable in length. What’s the minimal blue fraction?
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Don Quixote and the windmill
Don Quixote is approaching a windmill. The sails of length √2 are attached to a point that is 2 above eye level. What is the maximum vertical angle that Don Quixote perceives as he moves forward?
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Whiskey on the rocks
Two squares share a vertex. An isosceles triangle connects three others. What fraction is blue?
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The complicated jet
Two congruent squares inside a circle. The extended diagonals meet at the circle circumference. What’s their angle?
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The dark side
A quarter circle containing two touching semicircles cut by a chord. What fraction is brown?
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The carambole
Three touching congruent circles inscribed in an equilateral triangle. A small equilateral triangle inscribed in the centre space. What fraction is blue?
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The christmas tree
A triangle, a median and another cevian. What is the proportion of the two areas?
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The tip of the iceberg
A triangle with a 45° angle is placed inside a square as shown. What’s the area proportion of parts A and B?