If the circumcentre of a triangle lies on one of the sides then the orthocenter of the triangle lies on
एक त्रिभुज का परिकेन्द्र एक भुजा पर पड़ता है, तो त्रिभुज का लम्बकंन्द्र किस पर पड़ेगा?

Options

A. one of the vertices
B. on the same side of the triangle
C. outside the triangle
D. strictly inside the triangle

Explanation

To solve the problem, we need to understand the relationship between the circumcenter and orthocenter of a triangle, especially in the context of a right-angled triangle.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
We start by considering a triangle ABC, where angle C is a right angle (90 degrees). This makes triangle ABC a right-angled triangle.

**Hint**: Remember that in a right-angled triangle, the circumcenter is located at the midpoint of the hypotenuse.

2. **Identifying the Circumcenter**:
Since the circumcenter of the triangle lies on one of the sides, we can place it on the hypotenuse AB. In a right-angled triangle, the circumcenter is always at the midpoint of the hypotenuse.

**Hint**: The circumcenter is equidistant from all three vertices of the triangle.

3. **Finding the Orthocenter**:
The orthocenter of a triangle is the point where the altitudes of the triangle intersect. In a right-angled triangle, the orthocenter is located at the vertex of the right angle, which is point C in our case.

**Hint**: In a right-angled triangle, the orthocenter is always at the vertex where the right angle is located.

4. **Conclusion**:
Since the circumcenter lies on the hypotenuse (one of the sides), the orthocenter will lie at the vertex of the right angle, which is point C.

**Final Answer**: The orthocenter of the triangle lies at the vertex of the right angle.

### Summary:
If the circumcenter of a triangle lies on one of the sides, specifically in the case of a right-angled triangle, the orthocenter will lie at the vertex opposite to the hypotenuse, which is the right angle vertex.