I have to rotate a portion of a sector of the circle at an angle θ and then move the region along the tangent for a distance 'lateral offset' as given in the following image.

I used the below logic:
- Rotate the tangent point at angle θ.
- Calculate start and end angle of the sector using the width of the sector.
- Translate the the center of the circle with lateral offset in the direction of our target point
- Apply start and end angles from the new center point to filter out the translated sector region.
The idea is to move the center of the circle parallel to the tangent to identify the translated sector points. Is this approach correct? Is there any other optimal way to solve this problem?