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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The freight elevator
Tag: rectangle
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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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The dome tent
A rectangle with a diagonal and an inscribed semicircle. What is red : green : blue?
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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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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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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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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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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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The kissing circles
A rectangle with three touching quarter circles. What fraction of its area is coloured?
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Twin peaks
A rectangle with three line segments. What is the proportion yellow : red?