+185 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.
+23246 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 ...
