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The freight elevator

Four points A, B, C and D form a quadrilateral. Prove that it is a rectangle if and only if for an arbitrary point P we have PA2+PC2=PB2+PD2.

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Intermediate

The red sash

Two squares and a rectangle. What is area of the rectangle in terms of square sides a and b?

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Beginner

The dome tent

A rectangle with a diagonal and an inscribed semicircle. What is red : green : blue?

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Advanced

The crowded house

Three circles are inscribed in a rectangle. What is the area X in terms of A and B?

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Advanced

The letter box

A rectangle with a diameter and two inscribed squares. What is its area in terms of the square areas A and B?

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Beginner

The tornado

A quadrilateral covers exactly half of the area of a rectangle. Find the length x in terms of a, b and c.

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Advanced

The stuck boulder

A rectangle contains a circle wedged between two triangles. What is the circle radius in terms of triangle heights a and b?

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Beginner

Composition in red, blue and yellow

A rectangle containing red and blue squares and a yellow rectangle. What is the proportion red : (blue+yellow)?

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Beginner

The kissing circles

A rectangle with three touching quarter circles. What fraction of its area is coloured?

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Beginner

Twin peaks

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