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