A triangle cut by a line and four parallel line segments. Prove that green = red.
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Above the line
Tag: triangle
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Kazakov triangles
A circle with its centre and three triangles consisting of chords and radii. Express area X in terms of A, B and α.
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Angle chase
Two triangles are placed as shown. What is the angle α?
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Ice cream cone III
A triangle with its incircle and a cevian. What is red : yellow?
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In and out II
A couloured triangle and rectangle with extended sides and two circles. Prove that the triangle and the rectangle have equal areas.
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Side touches
Four triangles in a rectangle. The three red triangles have equal areas. What is blue : red?
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Centre of attraction III
Three congruent squares and an equilateral triangle. What is blue : orange?
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Compartments
An equilateral triangle with a cevian and two inscribed circles. What is yellow : red?
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The Grand Fir
A triangle, its circumcircle, circumcentre and two altitudes. What’s the angle α?
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The Simson split
A cyclic quadrilateral has side lengths a, c, j, and k. Three segments drop perpendicularly to two sides and one diagonal of the quad, forming the green and purple triangles between them. What is the ratio purple/green, in terms of a, c, j, k?