Two equilateral triangles share a vertex. What is the area of their overlap region?
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Jingle bells
Author: Rik D. Tangerman
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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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Lost in rotation
Four equilateral triangles inscribed in a fifth one. What fraction of the latter is coloured?
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Pulling the strings
Two rods of length x and y are connected by two strings with a knot exactly halfway. The rods are placed parallel both with uncrossed and crossed strings. The distance between the knots is measured as a and b respectively. Express x and y in terms of a and b.
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The dog ear
A square contains a triangle. What fraction of the square is red?
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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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Brothers in arms
The tangency points of two tangents of a circle are connected. Three perpendiculars are drawn from a point on the circle, of which two have a given length. What’s the proportion red : yellow?
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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 steam iron
The midpoints of the hypotenuse of a right triangle and a line segment are connected. What is the length x?
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David and Goliath
Two squares share a vertex. What’s the proportion blue : green?