这题如何解答---**Question Stem:** Given a triangle ABC, line segment AD bisects angle BAC, BD = 2CD, and BC = 4. Find the maximum value of the area of triangle ABC. **Chart/Diagram Description:** * **Type:** Geometric figure, specifically a triangle. * **Main Elements:** * **Points:** There are four labeled points: A, B, C, and D. * **Lines/Segments:** * Segment AB connects point A and point B. * Segment AC connects point A and point C. * Segment BC connects point B and point C, forming the base of the triangle. * Segment AD connects point A to point D. * **Relative Position:** Point D lies on the segment BC, between B and C. Point A is a vertex opposite to the side BC. * **Annotations:** There is a faint watermark text "数学大仙" (Shuxue Daxian, meaning "Math Immortal") located near point A.