The orthocentre of a triangle is the point where

Options

A. the medians meet
B. the altitudes meet
C. the right bisectors of the sides meet
D. the bisectors of the angles meet

Answer

To determine the orthocenter of a triangle, we follow these steps:

### Step-by-Step Solution:

1. **Identify the Triangle**: Begin by identifying the triangle with vertices labeled as A, B, and C.

2. **Draw the Altitudes**: For each vertex of the triangle, draw a line segment (altitude) that is perpendicular to the opposite side.
- From vertex A, draw an altitude to side BC.
- From vertex B, draw an altitude to side AC.
- From vertex C, draw an altitude to side AB.

3. **Locate the Intersection Point**: The orthocenter is defined as the point where all three altitudes intersect. This point can be inside the triangle, on the triangle, or outside the triangle depending on the type of triangle:
- In an acute triangle, the orthocenter is inside the triangle.
- In a right triangle, the orthocenter is at the vertex of the right angle.
- In an obtuse triangle, the orthocenter is outside the triangle.

4. **Conclusion**: The orthocenter of the triangle is the point where the three altitudes intersect.