Categories
Intermediate

The fez

A circle and a semicircle inside a square. What’s the length proportion of the two chords?

Categories
Beginner

The partial eclipse

Two circles and a radius connecting their centres. What is the length of the parallel chord?

Categories
Beginner

The color fan

Two congruent rectangles share a vertex. Given that the three coloured areas are equal, what is the width x?

Categories
Beginner

The cross

A rectangle of height 2 is crossed by two line segments at right angles. What is its width?

Categories
Intermediate

The bolete

Two semicircles and a square. If the smaller diameter is 24, what is the larger?

Categories
Intermediate

The arena

In a circular arena two contestants are leaving from points A and B. Their respective speeds are such that they would collide at point C, but just before they do they exchange directions. Then they hit the edge of the arena and return to their starting points. During the whole race, A and B move […]

Categories
Beginner

The delta wing

A triangle with a cevian. Two lengths are given. What length is x?

Categories
Intermediate

The magic mirror

You are standing in front of a mirror. Your shoulder width is 50 cm and your eyes are 6 cm apart. What is the minimum mirror width for a stereo view of yourself?

Categories
Intermediate

The ricochet

An isosceles triangle with base 10 and sides 13. What is the total length of the red line segments?

Categories
Intermediate

Triangular billiards

A ball track starts halfway the left side of an equilateral triangular billiard table having side length 2. After two bounces it arrives in the top corner. What’s the total track length?