A tangent to a circle is a line intersecting the circle at exactly one point. Can you prove that the line from the center of the circle to the point of tangency is perpendicular to the tangent line?

**Note:** The above diagram is not drawn to scale.

- \(\angle FEC = 45 ^\circ\)
- the well goes to the left of the fence
- make the area of \(FECD\) as large as possible?

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