An ellipse, two circles centred in its focal points, a chord and a tangent. What is the angle α?
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The lorgnette
Tag: ellipse
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Pushing the boundary
Two equilateral triangles are placed side by side. What’s the proportion green : red?
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The gyroscope
Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.
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The Pappus eggs
Three semicircles and a circle with their centres. Two orange ellipses with focal points in the semicircle centres (they share the middle one). Prove that their upper intersection point coincides with the circle centre.
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The sliding ladder
A ladder seen from the side is sliding down a wall. Prove that a fixed point on the ladder traces part of an ellipse.