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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’?

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## Spiegel im Spiegel

A triangle with an inscribed triangle. What fraction of the former does the latter cover in terms of lengths a, b, c, d, e and f?

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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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## Circular architecture

An equilateral triangle and two circles. The centre of the right circle is the triangle side midpoint. Both circle intersections lie on a triangle side. Prove that the three red circular arcs are congruent.

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## Out of focus

A semicircle with an inscribed triangle. Both circles are tangent to the semicircle, the diameter and one other triangle side. Prove that the line segment connecting the two shown tangency points is parallel to the diameter.

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## The sacrosanct circles

Two tangent circles and two tangent line segments meeting in a point on the outer circle. The tangency points are connected by a line segment of length x. What’s x in terms of a and b?

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