To find the length of HE given the information about circle center and radii, we can use the following observations:
- FC is a radius of the circle with a length of 20 m.
- FH is another line segment, which presumably also relates to the circle.
However, without more context or a diagram to clearly define how points F, H, and E interact with each other in relation to the circle, we cannot definitively calculate the length of HE.
If F is on the circumference of the circle and H is somewhere within, the relationship between these points is critical to determine HE.
If we assume H is a point along the line segment from F to C, and the positions of points E and H relate to the radius and the geometry of the circle, we could solve it analytically with more information.
However, if FC and FH represent distances that would help in establishing a geometric relationship, we cannot provide a definitive answer without the actual image or more context.
Given typical exam-style questions with such parameters, if you have to choose based on the provided options, let's note that:
- Distances often require basic geometric operations such as difference or similarity in triangles.
If we consider the relationship: If FH (12 m) is a distance that goes from F inward towards C, then HE can be calculated based on the remaining distance to the radius (20 m).
Thus: HE = FC - FH = 20 m - 12 m = 8 m
So, based on this calculation, the length of HE is 8 m.