Categories
Intermediate

The Pacman principle

In a circle, two congruent chords are connected in a point. A line segment is drawn through the circle center as shown, forming two angles. What is the proportion α : β?

Categories
Beginner

The askew envelope

In a square, an interior point is drawn with an angle to the top vertices of 120°. What’s the angle between the chords formed by the two arcs centered in these vertices?

Categories
Beginner

The diagonal dilemma

On two faces of a cube a diagonal is drawn that meet in the same vertex. What’s the angle between them?

Categories
Intermediate

The blockhat

Four congruent rectangles are placed in a hat-shaped configuration. What’s the angle between the lines connecting the opposite corners?

Categories
Advanced

The snowman mansion

A square and a half square are stacked in order to form a house-shaped quadrilateral. Inside two circles are closely packed. What’s the angle between the tangency points?

Categories
Intermediate

Balancing balls

Two touching circles are placed on top of a right triangle. What’s the angle between the chords connecting the tangency points?