The point of intersection of the common chords of three circles described on the three sides of a triangle as diameter is

Options

A. centroid of the triangle
B. orthocentre of the triangle
C. circumcentre of the triangle
D. incentre of the triangle

Explanation

To solve the problem of finding the point of intersection of the common chords of three circles described on the three sides of a triangle as diameters, we can follow these steps:

### Step-by-Step Solution:

1. **Draw Triangle ABC**: Start by sketching a triangle with vertices labeled as A, B, and C.

2. **Draw Circles**:
- Draw a circle with diameter AB. This circle will pass through points that create a right angle with the diameter AB.
- Draw another circle with diameter AC. This circle will also pass through points that create a right angle with the diameter AC.
- Finally, draw a circle with diameter BC. This circle will pass through points that create a right angle with the diameter BC.

3. **Identify Common Chords**:
- The common chord of the first two circles (with diameters AB and AC) will be a line segment that connects points on both circles, which we can denote as AE.
- The common chord of the second and third circles (with diameters AC and BC) will be another line segment, which we can denote as CG.
- The common chord of the first and third circles (with diameters AB and BC) will be denoted as BF.

4. **Determine the Intersection Point**:
- The three common chords AE, CG, and BF are actually the altitudes of triangle ABC.
- The point where these three altitudes intersect is known as the orthocenter of the triangle.

5. **Conclusion**: Therefore, the point of intersection of the common chords of the three circles described on the sides of triangle ABC as diameters is the orthocenter of the triangle.

### Final Answer:
The point of intersection of the common chords of the three circles described on the three sides of a triangle as diameter is the **orthocenter** of the triangle.

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