Finding normal vector on circles

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To calculate the normal vector of a circle, one must consider the radius vector at a specific point on the circumference, which points towards or away from the center. The tangent vector can be derived from the normal vector by rotating it 90 degrees. When the circle is rotated, the normal vector's direction may change, but it will still be aligned with the radius at the new point on the circle. Unlike straight planes, the normal vector varies at different points on the circle. Understanding these relationships is crucial for geometric calculations involving circles.
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Hi everyone.

Having a circle, knowing its center and radius, how can I calculate the normal vector? I need more information? Moreover, how can I calculate a tangent vector to the circle, knowing its center, radius and the normal vector?

If I rotate this circle, it is possible to calculate again the normal vector with the same direction? Because the normal vector can be pointing in opposite directions.

Thank you very much for your help.
 
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The normal vector at one point on the circle will be a different vector than the normal vector at some other point on the circle.

Only straight planes have the same normal vector at all its points.
 
The normal vector at any point on the circumference is along the radius vector to the point. It can be in either direction (outward or inward).
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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