请解答此题目---**Extracted Content:** **Source/Context Information:** 初一春下·数学小超市·沪教版·目标体系 **Question Number:** 31 **Question Stem:** 如图, △ABC 的两条角平分线 BD, CE 交于点 O. 若 ∠BAC = 40°, ∠ABC = 60°. 求证: 2BC - BE = AC. **Translation of Question Stem:** As shown in the figure, the two angle bisectors BD and CE of △ABC intersect at point O. If ∠BAC = 40°, ∠ABC = 60°. Prove: 2BC - BE = AC. **Geometric Figure Description:** * Type: Geometric figure, specifically a triangle with angle bisectors. * Main Elements: * Triangle ABC with vertices labeled A, B, C. * Line segment BD, originating from vertex B and intersecting side AC at point D. * Line segment CE, originating from vertex C and intersecting side AB at point E. * Point O, the intersection point of BD and CE, located inside the triangle. * Angles: ∠BAC is labeled as 40° near vertex A. ∠ABC is indicated. ∠BCA can be calculated. * Relative Positions: E is on side AB, D is on side AC. O is inside △ABC. **Given Information:** * BD bisects ∠ABC. * CE bisects ∠BCA. * BD and CE intersect at O. * ∠BAC = 40° * ∠ABC = 60° **To Prove:** 2BC - BE = AC

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