Categories
Beginner

Twin peaks

A rectangle with three line segments. What is the proportion yellow : red?

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Advanced

The ocean sunset

A semicircle is inscribed in a rectangle. What is the minimal covered fraction?

Categories
Beginner

The wall

Two congruent rectangles and squares. Proof that the four points are on one circle.

Categories
Intermediate

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?

Categories
Intermediate

Between the bars

Two parallel lines support two rectangles. Prove they have equal area.

Categories
Beginner

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?

Categories
Intermediate

The crazy diamond

Three rectangles and four triangles. Given that the red triangles have equal area, prove that the blue rectangles are similar.

Categories
Intermediate

The rolling mill

A rectangle with a semicircle, a quarter circle and a common tangent. What fraction is blue?

Categories
Intermediate

The holiday home

An isosceles triangle, a rectangle and two diagonals. What is the proportion green : blue?

Categories
Intermediate

The cleaver

Four squares, a rectangle and a circle. What is the proportion brown : grey?