Two tangent circles and two line segments of given length crossing at right angles at the tangency point. One of the line segments is parallel to a common tangent. What’s the total area?
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Velocipede III
Tag: circle
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The rolling stones
If you roll a circle down a parabola, small circles can roll all the way down and up, whereas large circles get stuck between the sides at some point. What is the transition radius? In other words, what’s the maximum circle that keeps on rolling?
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The end of the tunnel
Two semicircles and two congruent triangles with a side of length 2. What’s the brown area?
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The rocking cradle
A semicircle and an interior circle are tangent to each other. The chord towards the tangency point is divided in segments of length 1 and 2. What is the pink area?
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Caught in the middle
Two circles support a triangle. Prove it is equilateral.
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The monk’s hood
Two similar triangles inside a semicircle. What’s the angle?
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Mars rover has landed
Two semicircles and two right triangles. What fraction of the large triangle does the small one cover?
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The observatory dome
A semicircle with a radius, a chord and an altitude. What is the angle?
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The PowerPoint
A point lies 8 from the centre of a circle of radius 6. The angle α is variable. What’s the maximum triangle area?
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The toucan
Two congruent right triangles inscribed in a circle. The circle centre lies on one of the hypotenuses. What’s the angle?