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Sagot :
Mathematical proofs are used to determine if a mathematical statement is true or not.
See below for the proof of: [tex]\mathbf{PQ + RS + TU = QR + ST + UP}[/tex]
From the question (see attachment), we understand that: the three circles are congruent
This means that:
- The radii of the three circles are the same
- The length of the tangents are the same
Using the above highlights, we can conclude that:
- [tex]\mathbf{UP = TU}[/tex]
- [tex]\mathbf{ST =PQ}[/tex]
- [tex]\mathbf{QR = RS}[/tex]
Add ST to both sides of [tex]\mathbf{UP = TU}[/tex]
[tex]\mathbf{ST + UP = ST + TU}[/tex]
By substitution property of equality; substitute [tex]\mathbf{ST =PQ}[/tex]
[tex]\mathbf{ST + UP = PQ + TU}[/tex]
Add QR to both sides of [tex]\mathbf{ST + UP = PQ + TU}[/tex]
[tex]\mathbf{QR + ST + UP = QR + PQ + TU}[/tex]
By substitution property of equality; substitute [tex]\mathbf{QR = RS}[/tex]
[tex]\mathbf{QR + ST + UP = RS + PQ + TU}[/tex]
Rewrite as:
[tex]\mathbf{QR + ST + UP =PQ + RS + TU}[/tex]
Hence, the sums of the lengths of three pairs of not immediately adjacent sides of this hexagon have been proved to be equal
Read more about mathematical proofs at:
https://brainly.com/question/843621
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