A triangle with its circumscribed circle and a smaller intersecting circle. The two intersection points and the circumcentre are shown. What’s the proportion red : green?
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Two hemispheres
Tag: circle
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The new moon
A circle with two tangents, two chords and a secant. Prove that red and green are parallel.
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The wedge
A trapezium with its inscribed circle. Two tangency points are shown. What’s red / blue – yellow / green?
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The fish trap
Two intersecting circles and two common tangents. Prove that α = β.
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Lines in the sand
Two intersecting circles and four chords. Prove that the red chords are parallel.
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The same channel
Two circles and two common tangents. Prove that the blue triangle is isosceles.
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Angel wings
A circle with four chords and a diameter. What’s the proportion blue : green?
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Cross the line
An equilateral triangle with two line segments crossing exactly on the semicircle. What is the proportion red : green?
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The steam locomotive
Two tangent circles, a chord towards the tangency point and a tangent. What’s the proportion a : b in terms of radii R and r?
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The inner circle
A triangle with its incircle. A line segment through two tangency points and one through the incentre. What’s the angle α?