A parabola and its directrix in red. Two tangents intersect at a point on the directrix. What’s the angle α?
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The grazing shot
Category: Advanced
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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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The new moon
A circle with two tangents, two chords and a secant. Prove that red and green are parallel.
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Slightly skewed
Two overlapping equilateral triangles with side lengths 1. What is the total red length?
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Angel wings
A circle with four chords and a diameter. What’s the proportion blue : green?
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The inner circle
A triangle with its incircle. A line segment through two tangency points and one through the incentre. What’s the angle α?
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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 sneak peek
A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?
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The golf ball
A circle and a triangle with two sides tangent to the circle and a side connecting the tangency points. The line segment of the circle centre to the triangle apex is shown. Prove that α = β.
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The rotary movement
Two arbitrarily placed congruent equilateral triangles. Out of all the possible rotations of the plane, for how many will the image of ABC be A’B’C’?