Question

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 the point of tangency. Determine the radius of the pond.

Answer 1

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Answer:

8 ft

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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Additional comment

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.