Two regular hexagons inscribed in a square. If the hexagons have side length a and b, what is the square’s side length?

# Tag: length

## En garde

An isosceles triangle with two altitudes dividing each other in segments of length 4 and 5. What is the total triangle area?

## The screwball ice cream

A circle of radius r touching both sides of a parabola having focal length a. A line segment tangent to the circle is split in two equal segments of length d. What is d in terms of r and a?

## The single parent holiday

An equilateral triangle containing two circles of given area and a common tangent divided in two. What is the proportion of the two parts?

## The fez

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

## The partial eclipse

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

## The color fan

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

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

## The bolete

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

## 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 […]