Answer:
19.5 feet
Step-by-step explanation:
I assume you mean 40 feet, not 4 feet.
Draw a picture of the pond and Angelo the alligator. Angelo is 25 feet from the edge of the pond. If we draw a tangent line from Angelo to the pond, the length of the tangent line is 40 feet.
Now draw a radius line from the center of the circle to the point of tangency; this is perpendicular to the tangent line. Draw another radius line from the center of the circle towards Angelo.
The result is a right triangle, where the legs are r and 40 feet, and the hypotenuse is r+25 feet.
Using Pythagorean theorem:
(r + 25)² = r² + 40²
r² + 50r + 25² = r² + 40²
50r + 25² = 40²
50r + 625 = 1600
50r = 975
r = 19.5
The radius of the pond is 19.5 feet.
