In triangle ABC, medians AD and CE have lengths 18 and 27 respectively, and AB = 24. The line CE is extended to meet the circumcircle of triangle ABC at point F. G is the centroid of the triangle. Which of the following statements are correct?

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b = 3 * sqrt(70). Median from A (to midpoint D of BC): mₐ² = (2b² + 2c² - a²)/4 = 324, so 2b² + 2*576 - a² = 1296 => 2b² - a² = 144...(1). Median from C (to midpoint E of AB): m_c² = (2a² + 2b² - c²)/4 = 729, so 2a² + 2b² - 576 = 2916 => 2a² + 2b² = 3492 => a² + b² = 1746...(2). From (1): 2b² - a² = 144 => a² = 2b² - 144. Substituting into (2): 2b² - 144 + b² = 1746 => 3b² = 1890 => b² = 630 => b = sqrt(630) = 3*sqrt(70). Then a² = 1746 - 630 = 1116, a = sqrt(1116) = 6*sqrt(31). Both A and B are correct. For option D: G divides CE in 2:1, so CG = 18, GE = 9. By power of a point or intersecting chords: GE * GF = GA * GD. GA = (2/3)*18 = 12, GD = 6. GE*GF = 12*6 = 72. GF = 72/9 = 8. EF = GE +

In triangle ABC, medians AD and CE have lengths 18 and 27 respectively, and AB = 24. The line CE is extended to meet the circumcircle of triangle ABC at point F. G is the centroid of the triangle. Which of the following statements are correct?

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