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Advanced

The christmas tree

A triangle, a median and another cevian. What is the proportion of the two areas?

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Intermediate

The bowtie

A square and two congruent isosceles triangles with variable top angle. What is the maximum fraction shaded?

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Intermediate

The inner triangle

A triangle and two medians. What fraction is shaded?

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Intermediate

The ace of diamonds

Four congruent right triangles form a rectangle. What fraction is red?

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Advanced

The tip of the iceberg

A triangle with a 45° angle is placed inside a square as shown. What’s the area proportion of parts A and B?

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Intermediate

The hunting horn

Two semicircles and four tangents. What’s the area of the orange rectangle?

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Intermediate

The rubber rotation

Two overlapping rectangles. What is the proportion of their areas? All triangles in the diagram are right.

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Beginner

The radio telescope

A square contains two triangles. What fraction of the square do they cover?

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Advanced

The Post-it note

Two unit squares (having side 1) are placed as shown. What is the total perimeter of the two red triangles?

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Beginner

The warning triangle

An equilateral triangle contains three congruent rectangles. Two distances on its base are given. What fraction is white?