解答---**Question Identification:** 6. [2024 湖北武汉东西湖区校级月考] **Question Stem:** 如图,已知△ABC 中, ∠A = 60°, BD, CE 是△ABC 的两条角平分线, BD, CE 相交于点 O, 试说明: BC = CD + BE. **Translated Question Stem:** As shown in the figure, in △ABC, it is known that ∠A = 60°, BD and CE are the two angle bisectors of △ABC, BD and CE intersect at point O. Please explain: BC = CD + BE. **Geometric Figure Description:** * **Type:** Geometric figure, specifically a triangle with internal line segments. * **Main Elements:** * **Shape:** Triangle ABC. * **Vertices:** Labeled A, B, C. * **Points:** Point D is on side AC, point E is on side AB, point O is inside the triangle. * **Lines:** Line segment BD connects vertex B to point D on AC. Line segment CE connects vertex C to point E on AB. BD and CE intersect at point O. * **Angles:** Angle at vertex A is labeled as 60°. Angle at vertex B is divided into two equal angles (∠ABD and ∠DBC) marked with double arcs. Angle at vertex C is divided into two equal angles (∠ACE and ∠ECB) marked with single arcs. * **Labels:** Vertices A, B, C. Points D, E, O. Angle A is labeled 60°. * **Relative Position:** D lies on AC, E lies on AB. O is the intersection point of BD and CE.