Geometry_Circles_How the heck am I supposed to figure this out??

Question

http://i53.photobucket.com/albums/g68/jec528/cirrrcle.jpg

Given: RT = (1/2)(RS) and TV = 9

Find: RT

Please help! :O

Answer 1

For the drawing in your link, the following relationship holds

RV * RT = RS^2

RV = RT + TV
RS = 2RT

by substitution (RT + TV)*RT = (2RT)^2

RT^2 + TV*RT = 4*RT^2
RT^2 + 9 RT = 4RT^2
9RT = 3RT^2
9 = 3 RT
RT = 3

Hope this helps.

Answer 2

The tangent secant theorem states that the length of the tangent segment squared is equal to the product of the secant segment and its external segment.

[ RS ] ² = [ RT + TV ] [ RT ]

[ 2x ] ² = [ x + 9 ] [ x ]

x = RT = 3

Answer 3

You are given a circle and RS tangent to the circle at S, and secant line RTV where TV is a chord of the circle.

RT = (1/2)RS
TV = 9

RS = 2*RT

By the secant-tangent theorem we have:

RS² = RT*RV = RT*(RT + TV) = RT*(RT + 9)
(2RT)² = RT*(RT + 9)
4RT² = RT*(RT + 9)
4RT = RT + 9
3RT = 9
RT = 3

Answer 4

letting RS =x, to make things easier.

X^2= 1/2 X ( X+9)
solving for X here,

you get, X=0 or, X= 6

check your formula from your geometry book, on circles.. if you are using jergensen, its chapter 9 ;)..

check your book for details..

Answer 5

rt=2.25 because through basic algebra and knowledge that
RS^2=(RT)(TV) [as states in the tangent-secant theorem]
(RS)^2=1/2
RS=2RT Substitution
So, (2RT)^2=9RT Square the quantity
4RT^2=9RT divide by 4
RT^2=(9/4)RT divide by RT
and you get
RT=9/4 or 2.25

Answer 6

You don't give enough information to answer the question. There has to be an equation minus one for each unknown. With the information given it is not solvable.

Answer 7

Use the formula RS^2 = RT*RV
Since RT = .5RS we have RS^2 =.5RS(.5RS+9)
RS^2 = .25RS^2 +4.5RS
.75RS^2 -4.5RS= 0
RS(.75RS-4.5)=0
.75RS = 4.5
RS = 4.5/.75 = 6
Rt=.5RS = .5*6 = 3

Answer 8

do you have more info?
If we change the angle of R, then we can get many answers.