Categories
Beginner

Squaring a rectangle

A regular hexagon, a square and a rectangle. What is the area proportion rectangle : square?

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Intermediate

A clear vision

A circle containing a regular pentagon and two equilateral triangles. All shown points are on the circle. What’s the angle α?

Categories
Intermediate

Star and stripes

Two concentric congruent squares and two red rectangles. What fraction of the total area is red?

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Advanced

The inner parallel

A cyclic quadrilateral with its diagonals and two altitudes. Prove that AB is parallel to EF.

Categories
Intermediate

Letting go

Two squares share a vertex. Three other vertices are collinear. What is the area proportion of the blue to the red square?

Categories
Beginner

Orange above

A square contains a right triangle. What fraction is orange?

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Intermediate

The double flag

Three tangent circles and a common tangent. The three tangency points are shown. What is α + β?

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Advanced

The door stop

A triangle with a cevian. What is α?

Categories
Beginner

Four to twelve

A regular dodecagon and a square share two vertices. What is the area proportion square : dodecagon?

Categories
Intermediate

The japanese progression

An isosceles trapezium with its inscribed circle. If the lengths are such that b-a=c-b=d-c, what is a : b : c : d?