In a circle, two congruent chords are connected in a point. A line segment is drawn through the circle center as shown, forming two angles. What is the proportion α : β?
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The Pacman principle
Tag: circle
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The velocipede
Two circles are embedded in a frame of size 9 x 8. What is their total area?
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The inner wheel
A wheel is placed inside another that has exactly twice its radius. If the inner wheel rolls around once without slipping, how many revolutions has it completed?
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The shark fin
An isosceles triangle is inscribed in a semicircle with one side along the diagonal and the top vertex somewhere on the semicircle. What’s the maximum fraction shaded?
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The snowman mansion
A square and a half square are stacked in order to form a house-shaped quadrilateral. Inside two circles are closely packed. What’s the angle between the tangency points?
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Balancing balls
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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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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Moon over mountains
A rectangular frame encloses two congruent equilateral triangles and a unit circle. What is difference between width and height of the rectangle?
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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?