9514 1404 393
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.
__
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.
