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?

radius ≈ 43. 30 ft

Step-by-step explanation:

A tangent to a circle is a straight line that touches the circle at one point. This is known as the point of tangency.  The line of tangency forms an angle 90°.

The distance from you to a point of tangency = 25 ft.

Distance from you to the center of the circle = 50 ft

The illustration forms a right angle triangle.

distance from you to the center of the circle is the hypotenuse and distance from you to the point of tangency is the opposite side. The adjacent side is the radius.

Using Pythagoras theorem

c² = a² + b²

where

c = 50 ft

a = 25 ft

b = ?

c² = a² + b²

50² = 25² + b²

2500 - 625 = b²

b² = 1875

square root both sides

b = √1875

b = 43.3012701892

b = 43. 30 ft

radius ≈ 43. 30 ft