The ortho centre of a right angled triangle lies

Options

A. outside the triangle
B. at the right angular vertex
C. on its hypotenuse
D. within the triangle

Answer

To solve the question regarding the location of the orthocenter in a right-angled triangle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Right-Angled Triangle**:
- Draw a right-angled triangle and label its vertices as A, B, and C, where angle B is the right angle (90 degrees).

2. **Definition of the Orthocenter**:
- The orthocenter of a triangle is defined as the point where all the altitudes of the triangle intersect. An altitude is a perpendicular line drawn from a vertex to the opposite side.

3. **Drawing the Altitudes**:
- From vertex A, draw a perpendicular line to side BC. This line represents the altitude from A.
- From vertex C, draw a perpendicular line to side AB. This line represents the altitude from C.
- The altitude from vertex B is not necessary to draw because it will coincide with side AC (the right angle).

4. **Finding the Intersection**:
- Observe where the altitudes from A and C intersect. Since the altitude from B lies along side AC, the intersection of the altitudes from A and C will be at point B itself.

5. **Conclusion**:
- Therefore, in a right-angled triangle, the orthocenter lies at the vertex of the right angle. In this case, the orthocenter is located at point B.

### Final Answer:
The orthocenter of a right-angled triangle lies at the vertex of the right angle.

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