Question

You stand at point C and look at an aquarium tank. Calculate the radius of the aquarium tank.

Answer 1

Answer:

8.25

Step-by-step explanation:

DC = 14ft

AC = 8ft + the diametre

Lets use d for diametre

The equation we are using is the Segments of Secants and Tangents Theorem, which is $DC^{2}$ = 8ft (or the outside segment) * AC (the whole segment)

$14^{2}$ = 8 * (8 + d)

196 = 64 + 8d

Subtract 64 from 196 to get: 132 = 8d

Divide 8 from 132 to get: d = 16.5

Now the diametre is 16.5, but the radius is half the diametre, so now you have to do: 16.5 / 2

So the radius would end up being 8.25

Answer 2

Answer:

The radius of the aquarium tank is $8.25\ ft$

Step-by-step explanation:

we know that

Applying the Tangent Secant Theorem

$DC^{2}=AC*8$

we have that

$AC=(D+8)\ ft$

$DC=14\ ft$

substitute

$14^{2}=(D+8)*8$

$196=8D+64$

Solve for D

$8D=196-64$

$8D=132$

$D=16.5\ ft$

Find the radius

The radius is half the diameter

$r=16.5/2=8.25\ ft$