Question

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

Answer 1

8.25

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

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

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`