A triangle containing three tangent semicircles with diameters a, b and c. Three line segments pass through the red tangency points. What is the triangle perimeter?
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The triple airbag
Month: September 2022
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The grazing shot
A parabola and its directrix in red. Two tangents intersect at a point on the directrix. What’s the angle α?
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The iron curtain
A parallelogram ABCD with a circle and a diameter CE. Prove that point E is the orthocentre of triangle ABD.
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Worlds colliding
Two intersecting circles and a circle passing through both their centres and their intersection points. What’s the angle α?
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The common triangle
Two semicircles contain a triangle. The centre of the right semicircle is shown. Prove that the triangle is isosceles.
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At navel level
Two equilateral triangles share a vertex. The centre of the larger one is aligned with the midpoint of a side of the smaller one. What is green : red?
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Sharing is caring
Three equilateral triangles and three shared vertices. What’s the proportion blue : green?
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The fried egg
Two concentric circles and two tangents. What is the yellow fraction?
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Lopsided
The apex of a parabola is the shared vertex of two rectangles. Proof that the rectangles are similar.
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Harmonic proportions
A trapezium with its diagonals and a parallel line segment. Prove that yellow : purple = blue : red.