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For **Part A**, the question is asking about the concurrency of the angle bisectors of a triangle. The **angle bisectors** of a triangle are lines or segments that divide each angle of the triangle into two equal parts. The point where the three angle bisectors of a triangle meet is called the **incenter**.

The incenter is always located inside the triangle, and it is the center of the triangle's incircle (a circle that touches all three sides of the triangle). This holds true for **acute**, **right**, and **obtuse triangles**. Hence, the correct answer for Part A is:

- **They are always concurrent.**

For **Part B**, the question is asking if it's possible for the intersection of the angle bisectors (the incenter) to be outside the triangle. Since the incenter is always the center of the inscribed circle and is always located inside the triangle, it **cannot** be outside the triangle. Therefore, the answer to Part B is:

- **No, it is not possible for the intersection of the angle bisectors to be outside the triangle** because the incenter is always inside the triangle.

Let me know if you want more details or have further questions!

Here are 5 follow-up questions:
1. What is the difference between the incenter and the circumcenter of a triangle?
2. Can the incenter ever coincide with the centroid of a triangle?
3. What is the relationship between the incenter and the triangle’s area?
4. How do you construct the incenter using a compass and straightedge?
5. What are the properties of the incircle?

**Tip:** Incenter always stays inside the triangle because it is equidistant from all sides of the triangle.

Move the vertices of the triangle. What is true about the angle bisectors?

Explore the concurrency of angle bisectors in triangles. Learn how the incenter is always formed at the intersection of the bisectors, regardless of whether the triangle is acute, right, or obtuse. Suitable for students in Grades 8-10.

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