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Advanced

The complicated jet

Two congruent squares inside a circle. The extended diagonals meet at the circle circumference. What’s their angle?

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Intermediate

The drop shadow

Two congruent squares share a vertex. What’s the angle α?

Categories
Intermediate

The white flags

Three congruent squares and three shared vertices. What fraction is blue?

Categories
Intermediate

The divided diagonal

A square diagonal is divided in three by a 45-degree angle. Two pieces are given, what is the length of the third?

Categories
Beginner

New Year 2021

Three squares are placed as shown. Given that the green areas are equal, what is the side length of the orange square?

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Intermediate

Domino day

Three congruent rectangles consisting of two squares each are placed as shown. What is the blue area?

Categories
Intermediate

The eye of the beholder

A square and two equilateral triangles inside and touching a circle. What’s the angle α?

Categories
Intermediate

The bowtie

A square and two congruent isosceles triangles with variable top angle. What is the maximum fraction shaded?

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Advanced

The tip of the iceberg

A triangle with a 45° angle is placed inside a square as shown. What’s the area proportion of parts A and B?

Categories
Beginner

The radio telescope

A square contains two triangles. What fraction of the square do they cover?