Categories
Beginner

The cross

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

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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 at constant but not necessarily equal speeds. Which contestant returns to his starting point first?

Categories
Beginner

The delta wing

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

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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?

Categories
Intermediate

The divided diagonal

A square diagonal is divided in three by a 45-degree angle. Two pieces are given, what is the length of the third?

Categories
Beginner

The parquet floor

A unit rhombus is surrounded by four congruent parallelograms. All five quadrilaterals have equal area. What are the parallelogram sides x and y?

Categories
Beginner

New Year 2021

Three squares are placed as shown. Given that the green areas are equal, what is the side length of the orange square?