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

Options

A. orthocentre
B. circumcentre
C. incentre
D. centroid

Answer

To solve the question regarding the radical center of three circles described on the three sides of a triangle as diameters, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We are given a triangle with vertices A, B, and C. We need to consider the circles that are formed using the sides of the triangle as diameters.

2. **Identify the Circles**: The circles are formed as follows:
- Circle 1: Diameter AB
- Circle 2: Diameter BC
- Circle 3: Diameter CA

3. **Properties of the Circles**: Each circle will have its center at the midpoint of the respective diameter. The radius of each circle will be half the length of the diameter.

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

5. **Using a Known Property**: A known property in geometry states that the radical center of the circles described on the sides of a triangle as diameters is the orthocenter of the triangle.

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

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