Question

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.

Answer 1

9514 1404 393

Answer:

28 feet

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.