+0  
 
+3
70
1
avatar+156 

Let TU and VW be chords of a circle, which intersect at S, as shown. If ST=3, TU=15, and VW=3, then find SW.


 

 Aug 6, 2020
 #1
avatar+21953 
+1

If you were to draw UV and TW, you would create triangle(SUV) and triangle(SWT).

By AA, triangle(SUV) is similar to triangle(SWT).

Therefore:  SU / SV  =  SW / ST     --->     SU · ST  =  SW · SV

 

Let  SV = x,  then  SW = x + 3.

 

SU · ST  =  SW · SV     --->     ( 18 )( 3 )  =  ( x + 3 )( x )

                                      --->               54  =  x2 + 3x

                                      --->                 0  =  x2 + 3x - 54

                                      --->                 0  =  (x + 9)(x - 6)

--->   x  =  6

 

From here, you can find the value of SW ...

 Aug 7, 2020

44 Online Users

avatar
avatar
avatar
avatar
avatar
avatar
avatar
avatar
avatar