A semicircle, a square and an isosceles triangle. What’s the angle α?
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The Eightfold Path
Category: Advanced
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Fun with flags
A triangle with two cevians. What is d/c-b/a?
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The Olympic bowl
A parabola is tangent to the equal sides of an isosceles triangle in its equal vertices. Another tangent is drawn as shown. Prove that the red line segments are congruent.
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As above, so below
A semicircle, a square, a triangle and two circles. A centre and a tangency point are highlighted. Prove that the circles are congruent.
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Mind the gap
A regular hexagon with an equilateral triangle sharing a vertex and having a vertex somewhere along the opposite side. What is the maximum length of line segment g?
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The crowded house
Three circles are inscribed in a rectangle. What is the area X in terms of A and B?
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The letter box
A rectangle with a diameter and two inscribed squares. What is its area in terms of the square areas A and B?
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A close encounter
Two semicircles are tangent to each other’s diameter. Are the line segments connecting their corners parallel?
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The extra large
A triangle with a cevian splitting its base in parts of length 2 and 1. What is the angle α?
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The stuck boulder
A rectangle contains a circle wedged between two triangles. What is the circle radius in terms of triangle heights a and b?