Nine Points Around a Triangle
Difficulty: Medium · Topics: Geometry, Vectors, Triangles
Uchburchak atrofidagi to‘qqiz nuqta
The points dividing each side of the equilateral triangle ABC into four equal parts are labelled D 1, D 2, D 3, …, D 9 in order around the triangle, starting from the point on the side AB nearest to A.
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If
≤ft overrightarrowD 1D 2+overrightarrowD 1D 3+overrightarrowD 1D 4+·s+overrightarrowD 1D 9 =9√21,
find the perimeter of the equilateral triangle ABC.
Muntazam ABC uchburchakning har bir tomonini to‘rtta teng qismga bo‘luvchi nuqtalar AB tomondagi A ga eng yaqin nuqtadan boshlab uchburchak atrofida tartib bilan D 1, D 2, D 3, …, D 9 deb belgilangan.
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Agar
≤ft overrightarrowD 1D 2+overrightarrowD 1D 3+overrightarrowD 1D 4+·s+overrightarrowD 1D 9 =9√21
bo‘lsa, muntazam ABC uchburchakning perimetrini toping.