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.
Answered yesterday by geno
https://web2.0calc.com/questions/geometry-please-help-explain#r1
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.
Euclid's Proposition 36, book 3: https://mathcs.clarku.edu/~djoyce/java/elements/bookIII/propIII36.html
Euclid's Proposition 36, book 3 states that ST*SU=SW*SV
Since we want to find SW to get SV, we can change SW to x.
We already know the other lengths:
ST=3
SU=18
SW=x
SV=x-3
So, 3(18)=x(x-3).
From here, we see that when expanded, this becomes 54=x^2-3x.
Solving the quadratic, we see that SW is 12, therefore SV is 9.
EDIT: Or, you could refer to the link in @above....(the steps and reasoning are slightly different, you can look there if you do not understand what I am talking about...)
:)