The radical centre of the three circles described on the three sides of a triangle as diameter is ......... of the triangle

Options

A. centroid
B. orthocentre
C. circum centre
D. incentre

Answer

To solve the problem, we need to determine the radical center of the three circles that are described on the sides of a triangle as diameters. Here’s a step-by-step breakdown of the solution:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to identify the radical center of three circles that are constructed using the sides of a triangle as diameters.

2. **Identify the Circles**: For a triangle ABC, we can construct three circles:
- Circle on side AB as diameter.
- Circle on side BC as diameter.
- Circle on side CA as diameter.

3. **Radical Axes**: The radical axis of two circles is the locus of points that have equal power with respect to both circles. The radical center is the point where the radical axes of the three circles intersect.

4. **Properties of the Circles**: When circles are constructed on the sides of a triangle as diameters, the radical center can be determined using geometric properties of the triangle.

5. **Locate the Radical Center**: It is a known geometric fact that the radical center of the circles described on the sides of a triangle as diameters coincides with the orthocenter of the triangle.

6. **Conclusion**: Therefore, the radical center of the three circles described on the three sides of the triangle as diameters is the orthocenter of the triangle.

### Final Answer:
The radical center of the three circles described on the three sides of a triangle as diameter is the **orthocenter** of the triangle.

---