Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.
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The gyroscope
Tag: parallelogram
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The beam in your eye
Three parallelograms are inscribed in a circle. Prove that the common red vertex is the orthocentre of the dashed triangle.
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The iron curtain
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 crazy quilt
A parallelogram is divided into several areas. What is the area X of the blue trapezium?
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Out of proportion
An equilateral triangle containing a parallelogram, another equilateral triangle and a circular arc that is tangent in its base vertices. What is the proportion pink : blue?
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Silent circle
A large triangle with one side tangent to a circle. The tangency point is the vertex of a blue parallelogram. What is the red area?
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The orange belt
Three squares and three shared vertices. Prove that the orange quadrilateral is in fact a parallelogram.
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The skyscraper
A blue parallelogram with an extended diagonal. What is the proportion green : orange?
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The first cut
Using one straight cut, divide this triangle in two pieces. Paste them together to form a parallelogram with perimeter 19.
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The balance sheet
A unit square and a parallelogram. What’s the area of the latter?