A triangle and its circumcircle. What is red : blue?
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Colour coating
Tag: length
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The shadow side
A triangle with sides of length a and c is divided by a cevian of length b. What is brown : yellow in terms of a, b and c?
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Slippery slope II
The V is symmetric with respect to the vertical. Prove the algebraic relationship between the various segment lengths indicated by letters.
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Compromise point
The angles ABD and CBD’ are equal. A circle with diameter BD intersects AB and BC at F and H. Show red = blue (FJ = HJ) when J is the midpoint of DD’.
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Peaucellier pincers
The orange and blue segment lengths are fixed, the pivot point A and the purple line are fixed, and D slides up and down a fixed green line. Show that the intersection point G does not move.
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Four cycle motor
If the blue circle has unit radius and AC = s, what is the diameter of the red circle? (The moving green triangles have two vertices on the blue circle and right angles at M (on the red circle) and at C.)
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Windshield wipers II
A regular hexagon and a circular arc with its centre. What is the length of the red tangent line segment?
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Harmonious symmetry
Tangents to a circle intersect, and another line is drawn through that intersection. Show that the products of opposite sides of the blue quadrilateral are equal.
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Velocipede IV
Two circles with three common tangents. The smaller radius is extended as shown. Express the extension length x in terms of R and r.
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Miracle multiplication with pentagons
Seven regular pentagons connect as shown. Show that C is the midpoint of the line segment FS.