1. **Stating the problem:** We have a circle tangent to a vertical line at point F and tangent to a diagonal line starting from point G forming a 75° angle at point H. The radius of the circle intersects the diagonal line between points a and H. 2. **Understanding tangency and angles:** A circle tangent to a line means the radius at the point of tangency is perpendicular to that line. 3. **Key formula:** The radius is perpendicular to the tangent line at the point of tangency. If the diagonal line forms a 75° angle with the horizontal, the radius to the tangent point on this line will form a 15° angle with the horizontal (since radius is perpendicular to tangent line, and 90° - 75° = 15°). 4. **Using trigonometry:** If we denote the radius as $r$, then the horizontal and vertical components of the radius vector to the tangent point on the diagonal line are $r\cos 15^\circ$ and $r\sin 15^\circ$ respectively. 5. **Circle tangent to vertical line at F:** The circle touches the vertical line at F, so the center of the circle lies horizontally $r$ units away from the vertical line. 6. **Conclusion:** The center of the circle is located at a horizontal distance $r$ from the vertical line and lies on a line forming a 15° angle with the horizontal from the tangent point on the diagonal line. Since the problem does not provide numeric values for $r$ or coordinates, this is the geometric relationship and position of the circle's center relative to the given lines and points.