请根据这个图片帮我制作一个讲解初中几何《角平分线+飞镖模型》,标题就叫:角平分线+飞镖模型---**Overall Title:** 模型三 “角平分线+飞镖”模型 (Model 3 "Angle Bisector + Dart" Model)
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**Section 1: 内内飞镖 (Inner Dart)**
**Chart/Diagram Description:**
* **Type:** Geometric figure (Triangle with an internal point).
* **Main Elements:**
* **Shapes:** A large triangle labeled ABC. Inside this triangle, there is an internal point P.
* **Lines:** Straight line segments form the sides of triangle ABC (AB, BC, CA). Straight line segments connect point P to vertices B and C (BP, CP).
* **Points:** Labeled vertices A, B, C. Labeled internal point P.
* **Relative Position:** Point P is located inside triangle ABC.
**Textual Information (Problem Statement/Condition):**
BP、CP 分别是 ∠ABC 和 ∠ACB 的角平分线,则:∠P = 90° + 1/2 ∠A
(Translation: BP and CP are the angle bisectors of ∠ABC and ∠ACB respectively, then: ∠P = 90° + 1/2 ∠A)
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**Section 2: 证明 (Proof)**
**Textual Information (Proof Steps):**
根据飞镖模型的结论可知:
(Translation: According to the conclusion of the dart model, it is known that:)
∠P = ∠A + ∠ABP + ∠ACP
∵ BP、CP 分别是 ∠ABC 和 ∠ACB 的角平分线
(Translation: ∵ BP and CP are the angle bisectors of ∠ABC and ∠ACB respectively)
∴ ∠ABP + ∠ACP
= 1/2 (∠ABC + ∠ACB)
= 1/2 (180° - ∠A)
∴ ∠P = 90° + 1/2 ∠A