讲解下这个题目---**Question Number:** (3) **Question Stem:** 如图, 在△ABC中, AD是∠BAC的外角平分线, P是AD上异于A的任意一点, 设PB = m, PC = n, AB = c, AC = b, 比较m + n与b + c的大小关系. **Translation of Question Stem:** As shown in the figure, in △ABC, AD is the angle bisector of the exterior angle of ∠BAC, P is any point on AD different from A. Let PB = m, PC = n, AB = c, AC = b. Compare the relationship between m + n and b + c. **Diagram Description:** * **Type:** Geometric figure. * **Elements:** * Triangle ABC. Points A, B, and C are vertices. * Line AD: A ray extending from A, forming the angle bisector of the exterior angle of ∠BAC. The exterior angle is formed by extending the line segment CA beyond A. * Point P: A point located on the line AD, distinct from point A. * Line segments: AB, AC, BC, AD, PB, PC. * **Labels:** * Vertices: A, B, C, D. * Point P. * Length labels mentioned in the text: PB=m, PC=n, AB=c, AC=b. These labels are not explicitly written next to the segments in the diagram, but the segments PB, PC, AB, AC are depicted. * **Relative Positions:** * B, C, and D appear to be collinear, with C between B and D. This suggests that the line segment CD is an extension of BC or BC is part of the line BD. However, AD is the bisector of the *exterior* angle at A. The diagram shows AD extending away from the triangle on the same side as the extension of CA. * P is on the line AD. * PB and PC are line segments connecting point P to vertices B and C of the triangle ABC. * **Angles:** AD bisects the exterior angle of ∠BAC. This exterior angle is formed by the extension of CA and the line AB. In the diagram, the extension of CA is not explicitly drawn as a dashed line or similar, but the line containing AD appears to extend from A such that AD bisects the angle formed by AB and this extended line. The point D is shown on this line. **Mathematical Notations:** * △ABC: Triangle ABC * ∠BAC: Angle BAC * AD: Line AD * PB = m: Length of segment PB is m * PC = n: Length of segment PC is n * AB = c: Length of segment AB is c * AC = b: Length of segment AC is b * m + n: Sum of lengths m and n * b + c: Sum of lengths b and c **Question Asked:** Compare the relationship between m + n and b + c. (i.e., is m+n > b+c, m+n < b+c, or m+n = b+c?)