Categories
Beginner

The punctured hexagon

A regular hexagon, a square and an equilateral triangle. Show that the top vertex of the triangle is on the hexagon circumcircle.

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Intermediate

Four six four

A regular hexagon and two similar rectangles. What fraction is green?

Categories
Intermediate

Six four

A regular hexagon and an inscribed tilted rectangle. What is the angle α?

Categories
Intermediate

Ball of yarn

A cyclic hexagon has concurrent cross diagonals. What is the ratio of the product of the orange sides compared to the product of the purple sides. (ace:bdf).

Categories
Advanced

The open roof

A regular hexagon with two line segments at right angles. What is the minimum of yellow : red?

Categories
Intermediate

The pumpkin

A regular hexagon and a circle centred in the blue point. What’s the angle α?

Categories
Intermediate

Tilted hourglass III

A regular hexagon, a circle through its red centre and two line segments. What’s blue : orange?

Categories
Intermediate

The hex division

A regular hexagon with two diagonals and two perpendiculars. What’s red : yellow?

Categories
Beginner

The see-through triangle

A regular hexagon and an equilateral triangle share a vertex. What is red : blue?

Categories
Intermediate

Go Orange

A regular hexagon, two diagonals and an orange equilateral triangle. What’s blue : orange : red?