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 fishing net

Two squares and two equilateral triangles. What fraction is hatched?

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Advanced

The lazy spider

A spider situated at point A on the outside of a cylinder with diameter 4 and height 3 is trying to get to a fly at point C on the complete opposite side as fast as possible. What is the shortest route?

Categories
Intermediate

The inner wheel

A wheel is placed inside another that has exactly twice its radius. If the inner wheel rolls around once without slipping, how many revolutions has it completed?

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Beginner

The broken window

A square is divided into triangles and quadrilaterals as shown. What fraction of the square area is covered by the shaded triangle?

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Advanced

The shark fin

An isosceles triangle is inscribed in a semicircle with one side along the diagonal and the top vertex somewhere on the semicircle. What’s the maximum fraction shaded?

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
Intermediate

The corner pocket

A snooker player wants to corner a ball starting from a point on one side and bouncing two times from the opposite sides. Given the dimensions of the table in the figure, what’s the length of the track the snooker ball travels?

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?