Question:medium

Let \( ABC \) be an equilateral triangle with orthocenter at the origin and the side \( BC \) lying on the line \( x+2\sqrt{2}\,y=4 \). If the coordinates of the vertex \( A \) are \( (\alpha,\beta) \), then the greatest integer less than or equal to \( |\alpha+\sqrt{2}\beta| \) is:

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In equilateral triangle coordinate problems, placing the centroid or orthocenter at the origin greatly simplifies calculations using symmetry.

Updated On: Mar 5, 2026

\(2\)
\(4\)
\(5\)
\(3\)

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The Correct Option is D

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