Categories
Intermediate

The pyramid perspective

Two congruent pyramids placed at different distances from the observer appear as equilateral triangles in a square frame. If the closest one is at 100 meter, how far is the distant pyramid?

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
Intermediate

The blue diamond

Two isosceles triangles are placed as shown. What is the proportion of the line segments a and b?

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?

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
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?

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Intermediate

The marble box

Two marbles of sizes π and 4π are enclosed in a rectangular box. What is the total area of the box?

Categories
Intermediate

The triangle tango

An isosceles triangle is attached to another triangle with a 60-degree angle as shown. Their opposite vertices are connected by a line segment of length 2. What is the area of the quadrilateral?

Categories
Intermediate

The Pentagon peaches

Five equally sized peaches are closely packed in a pentagon-shaped box. Their midpoints are the vertices of a smaller pentagon. What fraction is shaded?