Three semicircles and a circle all touching each other. The diameters of the two smallest semicircles are given. The large triangle connects three tangency points. What is the area of the green quadrilateral?

# Tag: quadrilateral

## The colour purple

A rectangle is split by two perpendicular lines. The four circles pass through vertices and intersection points. Their centres form a purple quadrilateral. What fraction of the large rectangle area does it cover?

## The stained glass

Two congruent rectangles are placed side by side. Two line segments form two coloured quadrilaterals and three triangles. What is the proportion purple : green?

## The fez

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

## The orange belt

Three squares and three shared vertices. Prove that the orange quadrilateral is in fact a parallelogram.

## The green field

A square is divided in two quadrilaterals of given area. What fraction of the square’s perimeter is red?

## Below the tree line

A triangle is split in two. What is the area of the green quadrilateral in terms of lengths a and b?

## The bigger picture

In a small square two perpendicular lines are drawn. A larger parallel square is constructed as shown. Prove it is a scaled copy of the smaller square but rotated 90° anticlockwise.

## La Flèche Wallonne

A triangle is divided in four. What is the black area?

## The attic room

A blue square is topped with a right triangle. Using line segments to the top, a green quadrilateral is constructed with at least two right angles. What is the area proportion green : blue?