Tag Archives: circle

New property of Bui chord circles – Tính chất mới của đường tròn dây cung Bui

November 12, 2011 Alexander Bogomolny published in Cut The Knot my “Pair of Siblings to Archimedes’ Twins“: http://www.cut-the-knot.org/Curriculum/Geometry/ArbelosBui.shtml (*) This pair later is collected by Floor van Lamoen in Online catalogue of Archimedean circles and named as “Bui chord circles“: … Continue reading

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Golden Ratio in Parabola – Tỷ Số Vàng trong Parabola

Point E is orthogonal projection of focus F on directrix of a parabola. The circle with diameter EF intersects the parabola at two points A, B. Results: Common chord AB divides diameter EF by golden ratio and of course AEF … Continue reading

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When I die…

When I die…  two points still make a line The constant distance still makes a circle The trilinears and the barycentrics Are still used on triangle center sites. When I die…  something is still mine! Khi tôi chết… hai điểm … Continue reading

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Magic Rectangle

Draw four horizontal parallel lines from up to down and distances between them are 3, 4 and 5 respectively. Draw four vertical parallel lines from left to right and distances between them are 6, 1 and 8 respectively. Of course … Continue reading

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Three Circles – One Inscribed Hexagon

I have found this simple method for construction of six concyclic points on sidelines of a triangle on April 6, 2006 and posted in Hyacinthos Geometry Forum. . Detail as following: . Theorem: If three circles concur at one Cevian … Continue reading

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