A town planner is building a fountain in the middle of a triangular shaped park and will place the fountain at the centroid of the triangle. A diagram of the triangular park shown by △ABD was used to determine the location of the fountain, which will be at point G. The longest median of the triangular park, AC¯¯¯¯¯, is 150 feet.

What is the distance from the corner of the park, at point A, to the fountain?

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