The answer is [A] 76 , but can someone please SHOW work on why it’s that answer .

Step-by-step explanation:

When a tangent line is drawn from Q to Z and then from Q to R, what happens that is the length of QZ and QR are the same.  So if QZ = 10, the QR = 10. The same occurs at every point outside the circle where a tangent line is drawn from that point to the circle. We are told that YX is 9.  That means that YZ is also 9. If XW is 9, then WV is also 9. Here's where the tricky part is. We are given the whole side length of UW as 17, but we need to know each individual part so we can eventually find the length of RS. So we'll keep going the way we were. If XW = 9, the WV = 9. That means that UV is 17 - 9 or 8. So UV = 8. That means that TU is also 8. THAT means that ST is 10 - 8 or 2. And if ST is 2, then RS is also 2.  Let's add it all together now:

QZ + ZY + YX + XW + WV + VU + UT + TS + SR + RQ

10 +    9 +   9 +     9 +    9 +     8 +   8 +    2 +   2 +   10 = 76

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step-by-step explanation:

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .