Multiple choice

AB is the diameter of a circle inscribed in a regular hexagon. CD is the diameter of the circumcircle of the same hexagon. If the area of the hexagon is 2019, then AB x CD is

  1. 2692

  2. 1346/2

  3. 2019

  4. None of these

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a regular hexagon with side a, area = (3 * sqrt(3) / 2) * a^2 = 2019. The inscribed circle diameter AB = sqrt(3) * a. The circumcircle diameter CD = 2a. AB * CD = (sqrt(3) * a) * (2a) = 2 * sqrt(3) * a^2. Since (3 * sqrt(3) / 2) * a^2 = 2019, a^2 = 4038 / (3 * sqrt(3)) = 1346 / sqrt(3). AB * CD = 2 * sqrt(3) * (1346 / sqrt(3)) = 2692.