Two touching circles are placed on top of a right triangle. What’s the angle between the chords connecting the tangency points?
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Balancing balls
Category: Intermediate
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The marble box
Two marbles of sizes π and 4π are enclosed in a rectangular box. What is the total area of the box?
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The triangle tango
An isosceles triangle is attached to another triangle with a 60-degree angle as shown. Their opposite vertices are connected by a line segment of length 2. What is the area of the quadrilateral?
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The Pentagon peaches
Five equally sized peaches are closely packed in a pentagon-shaped box. Their midpoints are the vertices of a smaller pentagon. What fraction is shaded?
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An Egyptian sunset
A semicircle touches a large equilateral triangle (area equals 9) at its apex and a smaller adjacent equilateral triangle (area equals 1) at its base as shown. What is the total red area?