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# 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. ​

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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 7, 2020

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Aug 7, 2020
edited by ElectricPavlov  Aug 7, 2020
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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...)

:)

Aug 7, 2020
edited by ilorty  Aug 7, 2020
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Wow thank you so much! You did more than needed which is incredible. Thank you!

Weiart000  Aug 10, 2020