Which of the following is not always inside a triangle?

Options

A. Incentre
B. Centroid
C. Intersection of altitudes
D. Intersectio of medians

Answer

To determine which of the following points is not always inside a triangle, we will analyze the four options provided: in-center, centroid, orthocenter, and circumcenter.

### Step-by-Step Solution:

1. **Identify the Points**:
- **In-center**: The point where the angle bisectors of a triangle intersect. It is always located inside the triangle.
- **Centroid**: The point where the medians of a triangle intersect. It is also always located inside the triangle.
- **Orthocenter**: The point where the altitudes of a triangle intersect. This point can be located inside or outside the triangle depending on the type of triangle.
- **Circumcenter**: The point where the perpendicular bisectors of the sides of a triangle intersect. This point can also be inside or outside the triangle.

2. **Analyze the Orthocenter**:
- In an **acute triangle**, the orthocenter lies inside the triangle.
- In a **right triangle**, the orthocenter lies on the triangle.
- In an **obtuse triangle**, the orthocenter lies outside the triangle.

3. **Conclusion**:
- Since the orthocenter can lie outside the triangle in the case of an obtuse triangle, it is the only point among the options that is not always inside the triangle.

### Final Answer:
The point that is not always inside a triangle is the **orthocenter**.

---