Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle α with the positive x-axis and the equations of its diagonals are (√(3) + 1)x + (√(3) - 1)y = 0 and (√(3) - 1)x - (√(3) + 1)y + 8√(3) = 0. Then a² is equal to:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q207

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumCoordinate Geometry478× since 2002

Let

a

be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle

\alpha

with the positive x-axis and the equations of its diagonals are

(\sqrt{3} + 1)x + (\sqrt{3} - 1)y = 0

and

(\sqrt{3} - 1)x - (\sqrt{3} + 1)y + 8\sqrt{3} = 0

. Then

a^2

is equal to: