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You are standing at a point, about 4 feet from a circular aquarium. If a tangent from your point to a point on the circle measures 10 feet, determine the length of the tanks’ radius

User Onyekachi Ezeoke
by
2.7k points

1 Answer

18 votes
18 votes

Answer:

10.5 feet

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

You are standing at a point, about 4 feet from a circular aquarium. If a tangent from-example-1
User Oiyio
by
2.8k points
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