Tag Archives: triangle

Using sum of squares triangle to prove sum of squares formula

We construct a number triangle from the integers 1, 2, 3, . . . n as follows. The first column contains 2*n-1 integers 1. The second column contains 2*n-3 integers 2. . . The last column contains only one integer … 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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Triangle Classification Diagram – Sơ đồ Phân loại Tam giác

In CTK arcticle Triangle Classification there is one interesting diagram of H. R. Jacobs. In one rectangle it represents all seven kinds of triangles of all classifications. I like it so much. I slightly change it to get one fixed … 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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My Avatar

Dear All My Friends, My Avatar is a image for very simple geometry problem: Given convex quadrilateral ABCD with M, N, P, Q are midpoints of sides AB, BC, CD, DA respectively. Four segments AP, BQ, CM, DN bound one … Continue reading

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