(2014 Jilin simulation) given that the right focus F of hyperbola x2a2 − y2b2 = 1 (a > 0, b > 0), the line x = A2C and its asymptote intersect at two points a and B, and △ ABF is an obtuse triangle, then the value range of hyperbolic eccentricity is () A. (3，+∞)B. (1，3)C. (2，+∞)D. (1，2)

(2014 Jilin simulation) given that the right focus F of hyperbola x2a2 − y2b2 = 1 (a > 0, b > 0), the line x = A2C and its asymptote intersect at two points a and B, and △ ABF is an obtuse triangle, then the value range of hyperbolic eccentricity is () A. (3，+∞)B. (1，3)C. (2，+∞)D. (1，2)

The asymptote equation of hyperbola x2a2-y2b2 = 1 (a ＞ 0, B ＞ 0) is y = ± Bax simultaneous equations y = ± baxx = A2C, and a (A2C, ABC), B (A2C, - ABC) are obtained. Let the intersection point D ∵ F of line x = A2C and X-axis be the right focus of the hyperbola, f (C, 0) ∵ △ ABF be an obtuse triangle, and AF = BF, ∵ AFB > 90 ° and ∵ AFD > 45 °, that is, DF < Da ∵ c-a2c < ABC, B < A, c2-a2 < A2 ∵ C2 The range of eccentricity is 1 < e < 2, so D is selected