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Angelo the Alligator is laying out next to a perfectly circular pond. He is 25 feet from the edge of the pond and 45 feet from the point of tangency. Determine the radius of the pond.

Angelo the Alligator is laying out next to a perfectly circular pond He is 25 feet from the edge of the pond and 45 feet from the point of tangency Determine th class=

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sqdancefan

9514 1404 393

Answer:

  28 feet

Step-by-step explanation:

Let r represent the radius of the pond. Then the Pythagorean theorem gives us the relation ...

  (25+r)² = r² + 45²

  625 +50r +r² = r² +2025

  50r = 1400 . . . . . . . . . . . . . subtract r²+625 from both sides

  r = 28 . . . . . . . . . . . divide by 50

The radius of the pond is 28 feet.

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