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Month: February 2024
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Balancing act II
Two squares share a vertex. What’s the angle α?
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Video: Wheel of fortune II
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Mind the steps
Three similar rectangles and a line segment. Express red in terms of blue and green.
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In and out
An obtuse triangle, of which α is the obtuse angle, with its incircle, two cevians and two tangents. Find a relation between α and β.
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Video: The Bedouin tent
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Angle versus height
What is the ratio orange/green?
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Video: Four six four
Two quarter-circles fit inside a square, and five circles fit inside the overlapped region, centred. What is the ratio of the (straight line) segment lengths red to blue? (The segments connect to points of tangency.)
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Pop you bubble
A square with a semicircle and a circle of equal radius. Their tangency point is shown. Prove that the red triangle is equilateral.