Angelica the Alligator is laying our next to a perfectly circular pond. She is 9 feet from the edge of the pond and 15 feet from
1 answer:
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Answer:
8 ft
Step-by-step explanation:
Consider the attached diagram.
The rule for secants and tangents tells us ...
(AC)(AB) = (AT)²
AC = AT²/AB = 15²/9 = 25
Then the diameter is ...
BC = AB - AC = 25 -9 = 16
The pond has a diameter of 16 ft, so a radius of 8 feet.
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<em>Additional comment</em>
Since point C is the nearest point on the edge of the pond to point A, it must lie on line AO. Hence BC must be a diameter.
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