If `PL , QM and RN` are the altitudes of `Delta PQR` whose orthocentre is O, then `P` is theorthocentre of:

Options

A. `Delta PQO`
B. `Delta PQL`
C. `Delta QLO`
D. `Delta QRO`

Answer

To solve the problem, we need to determine what triangle has P as its orthocenter given that PL, QM, and RN are the altitudes of triangle PQR, with O being the orthocenter of triangle PQR.

### Step-by-Step Solution:

1. **Understanding the Orthocenter**:
The orthocenter of a triangle is the point where the three altitudes intersect. In triangle PQR, the orthocenter is denoted as O.

2. **Identifying the Altitudes**:
The altitudes PL, QM, and RN are drawn from points P, Q, and R respectively, perpendicular to the opposite sides. This means:
- PL is the altitude from P to side QR.
- QM is the altitude from Q to side PR.
- RN is the altitude from R to side PQ.

3. **Finding the Orthocenter of Triangle QRO**:
We want to find a triangle where P is the orthocenter. In triangle PQR, since O is the orthocenter, we can consider triangle QRO.

4. **Analyzing Triangle QRO**:
In triangle QRO, the altitudes will be:
- From Q to side RO.
- From R to side QO.
- From O to side QR.
Since P is outside triangle QRO and is the orthocenter, it means that triangle QRO must be an obtuse triangle, where the orthocenter lies outside the triangle.

5. **Conclusion**:
Therefore, the triangle for which P is the orthocenter is triangle QRO.

### Final Answer:
P is the orthocenter of triangle QRO.