Answer:
10.5 feet
Step-by-step explanation:
You want to know the radius of a tank when the tangent from a point 4 ft from the tank is 10 ft long.
Secant relations
Two secants of a circle drawn from the same point have the same product of their lengths to the near and far intersection points with the circle.
When one of those secants degenerates to a tangent, the near and far points are the same point, and the product is the square of the tangent length.
Application
Referencing the attached diagram, we have ...
MA² = MB·MC
10² = 4·MC
100/4 = MC = 25
Solving for radius r, we have ...
MC = 4 +2r
25 -4 = 2r = 21 . . . . . subtract 4
r = 21/2 = 10.5 . . . . . divide by 2
The radius of the tank is 10.5 feet.
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Additional comment
The radius can also be found using the Pythagorean theorem:
10² +r² = (4+r)² . . . . . . . . . Pythagorean relation
100 +r² = 16 +8r +r² . . . . . expanded
84 = 8r . . . . . . . . . . . subtract 16+r²
10.5 = r . . . . . . . divide by 8
