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## Fan of cards

N coloured rectangular cards are arranged with a common vertex and common angle α between cards. If a single card has perimeter P, what is the perimeter of the coloured region, in terms of N, P, and α?

Extra condition: N and α are such that at least two edges of the bottom card are visible.

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## Shine your light

A quarter circle of radius 1, a rectangle touching the circle in an arbitrary point and a yellow quadrilateral. What is the minimal perimeter of this quadrilateral?

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## A light packing

A triangle containing two congruent squares. Each square has 1/3 the perimeter and 1/6 the area of the triangle. What’s the triangle side length proportion a : b : c?

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## Ceteris paribus

Three circles with their centres and a triangle ABC. Given that D is the midpoint of BC, prove that quadrilateral ABEF and triangle ECF have both equal perimeter and equal area.

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## Slightly skewed

Two overlapping equilateral triangles with side lengths 1. What is the total red length?

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## The green field

A square is divided in two quadrilaterals of given area. What fraction of the square’s perimeter is red?

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## The Post-it note

Two unit squares (having side 1) are placed as shown. What is the total perimeter of the two red triangles?