Categories
Beginner

Four five

A square and a regular pentagon share a vertex. What’s the angle α?

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Intermediate

Orthogonal partial eclipse

Two circles are orthogonal (tangents at intersections are perpendicular). How must the points A and B be related?

Categories
Intermediate

Folding to pyramid

A square and an equilateral triangle. The square is folded as shown. What is the angle α?

Categories
Beginner

Outside the pentagon II

A regular pentagon and two equilateral triangles. What’s the angle α?

Categories
Beginner

The boot

Two squares and some line segments. Find the relation between the angles α and β.

Categories
Intermediate

What’s your angle?

Six squares are placed as shown. What’s the angle α?

Categories
Beginner

Steam roller

Two intersecting circles. Express the lengths b and the common tangent d in terms of c (the distance between the centres) and the angles β and γ.

Categories
Beginner

Fair scoop

What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?

Categories
Intermediate

Six six four

Two regular hexagons and a square. What’s the angle α?

Categories
Beginner

Square offspring

Three squares and two line segments. What’s the angle α?