Question

Algebra Find the value of each variable using the given chord, secant, and tangent lengths. If the answer is not

a whole number, round to the nearest tenth.

Answer 1

15.
`x = 15`

17.
`c = 13.2`

19.
`x = 25.8`;
`y = 12.4`

Explanation:

15.
`20*6 = 8*x` (intersecting chord theorem)

Solve for x

`120 = 8x`

Divide both sides by 8

`15 = x`

`x = 15`

17.
`(11 + 20)*11 = (13 + c)*13` (two secants intersecting theorem)

Solve for c

`31*11 = 169 + 13c`

`341 = 169 + 13c`

Subtract 169 from each side

`341 - 169 = 169 + 13c - 169`

`172 = 13c`

Divide both sides by 13

`(172)/(13) = (13c)/(13)`

`13.2 = c` (nearest tenth)

19.
`(x + 5)*5 = (15 + 7)*7` (two secants intersecting theorem)

Solve for x

`5x + 25 = 22*7`

`5x + 25 = 154`

Subtract 25 from each side

`5x + 25 - 25 = 154 - 25`

`5x = 129`

Divide both sides by 5

`(5x)/(5) = (129)/(5)`

`x = 25.8` (nearest tenth)

`y^2 = 7*(15 + 7)` (tangent and secant theorem)

Solve for y

`y^2 = 7*22`

`y^2 = 154`

Take the Square root of both sides

`√(y^2) = √(154)`

`y = √(154)`

`y = 12.4` (nearest tenth)