Question

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:

• A. \(2\)
• B. \(4\)
• C. \(5\)
• D. \(3\)

Hint:

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

Answer 1

The Correct Option is D