A parallelogram ABCD with a circle and a diameter CE. Prove that point E is the orthocentre of triangle ABD.
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The iron curtain
Category: Intermediate
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Worlds colliding
Two intersecting circles and a circle passing through both their centres and their intersection points. What’s the angle α?
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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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Lopsided
The apex of a parabola is the shared vertex of two rectangles. Proof that the rectangles are similar.
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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 piercing
An equilateral triangle containing a right triangle and a line segment. What fraction is pink?
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The crazy quilt
A parallelogram is divided into several areas. What is the area X of the blue trapezium?
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The common focus
A parabola, its symmetry axis and a tangent. Yellow connects the focus to the intersection point. Red connects the focus to the tangency point. What’s yellow : red?
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Under the volcano
A square containing a right isosceles and an equilateral triangle. What’s the angle α?