Two semicircles contain a triangle. The centre of the right semicircle is shown. Prove that the triangle is isosceles.
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The common triangle
Tag: triangle
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At navel level
Two equilateral triangles share a vertex. The centre of the larger one is aligned with the midpoint of a side of the smaller one. What is green : red?
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Sharing is caring
Three equilateral triangles and three shared vertices. What’s the proportion blue : green?
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Harmonic proportions
A trapezium with its diagonals and a parallel line segment. Prove that yellow : purple = blue : red.
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The parallax effect
Two intersecting circles with a triangle that passes through their centres and an intersection point. What’s the angle α?
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The piercing
An equilateral triangle containing a right triangle and a line segment. What fraction is pink?
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The purple hat
A circle with three tangents forming an isosceles triangle. Two tangency points are shown. What is the proportion green : red?
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The bell tolls
An equilateral triangle inscribed in a rectangle. What is its area X in terms of triangle areas A and B?
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Under the volcano
A square containing a right isosceles and an equilateral triangle. What’s the angle α?
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The Pisa experiment
Four squares and an altitude to the top vertex form a right yellow traingle. What is the proportion yellow : green?