Two squares and two equilateral triangles. Prove that the red vertices also form an equilateral triangle.
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Hidden perfection
Month: June 2023
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Corner to corner
A rectangle inside a rectangle. What is the green area?
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The green diamond
Two equilateral triangles are placed side by side. The common (blue) side is extended. What is red : blue?
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Little red square
Two squares and a circle. The line through the big square centre and small square vertex is tangent to the circle. What is the red area?
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All-seeing eye
If the radius shrinks by the factor 1/2 for each smaller circle, what fraction of the whole area is represented by all the blue crescents (separated by the red crescents)? Assume the circles keep going inward forever.
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The ball pit
Two rectangles contain 6 congruent circles. The common rectangle side passes through the top centre. What’s yellow : red?
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Cycling of tangents
Four circles share one point. The quadrilateral has vertices which are intersections of pairs of circles, and three of its coloured edges are tangent to the circle of the same colour. Show that the fourth edge is also tangent to its circle.
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Shine your light
A quarter circle of radius 1, a rectangle touching the circle in an arbitrary point and a yellow quadrilateral. What is the minimal perimeter of this quadrilateral?
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The beehive
Three regular hexagons, one centre and a triangle. What fraction of the total area is orange?
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Launch the ball
Express the circle area in terms of the isosceles triangle area A and its side length a.