SOLUTION: <a href="http://tinypic.com" target="_blank"><img src="http://i42.tinypic.com/35mqty8.jpg" border="0" alt="Image and video hosting by TinyPic"></a> In the diagram, TS is tangent t

Algebra ->  Circles -> SOLUTION: <a href="http://tinypic.com" target="_blank"><img src="http://i42.tinypic.com/35mqty8.jpg" border="0" alt="Image and video hosting by TinyPic"></a> In the diagram, TS is tangent t      Log On


   

Question 179522: Image and video hosting by TinyPic
In the diagram, TS is tangent to the circle at S and TAY is a secant.
If TS = 2v3 (2 square roots of 3) and TA = 2, what is TY?
PLEASE HELP ME SOLVE FOR TY, ANY HELP IS APPRECIATED!
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Tangent-Secant Theorem (scroll down if you can't see the section)


Here's what the theorem says: If you have a tangent line PA which intersects with a secant line PD (where the point C is on the circle and a point on the secant line), then

PA%5E2=PC%2ACD (ie there's a ratio/connection between the sides of the tangent and secant segments)


So in this case, the formula becomes TS%5E2=TA%2AAY



TS%5E2=TA%2AAY Start with the given formula


%282%2Asqrt%283%29%29%5E2=2%2AAY Plug in TS=2%2Asqrt%283%29 and TA=2


12=2%2AAY Square 2%2Asqrt%283%29 to get


12%2F2=AY Divide both sides by 2 to isolate AY.


6=AY Divide.


So we get AY=6 which means that the length of segment AY is 6 units.


Now add TA to AY to get

TA%2BAY=TY


2%2B6=TY Plug in TA=2 (which is given) and AY=6 (which was just found)


8=TY Add


TY=8 Rearrange the equation


So the length of TY is 8 units