Question

You are standing 50 feet from the center of a circular swimming pool. The distance from you to a point of

tangency is 25 feet. What is the approximate radius of the pool?
Round to the nearest tenth.
radius =​

Answer 1

9514 1404 393

Answer:

43.3 ft

Explanation:

If r is the pool radius, the distance from my position to the nearest pool edge is (50-r) and the distance to the farthest pool edge is (50+r). The product of these distances is the square of the distance to the tangent point:

(50 -r)(50 +r) = 25²

2500 -625 = r² . . . . . . add r²-625

r = √1875 ≈ 43.301

The radius of the pool is approximately 43.3 feet.