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# Geometry Q

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For this problem: XY = 14, WX = 8, and WZ || "Line X" Find YZ

Jul 30, 2020
edited by Weiart000  Jul 30, 2020

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I have drawn this in GeoGebra and got the geometric solution of approx  9.4 (2 decimal places)

This does agree with guests answer.

Here is my pic.

You can click on the grab point G to change the size of the circle an you will see that the answer does not change (while the circle actually exists)

https://www.geogebra.org/classic/mb2b9dmg

Aug 2, 2020
edited by Melody  Aug 2, 2020
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Put another point V on the tangent, below X.

The angle VXY = angle XWY (angle on the circumference in the opposite segment), and also angle VXY = angle XZW (since the tangent at X is parallel to WZ), so angle XWY = angle XZW.

We have then two similar triangles, XWY, and XZW, (the angle at X is common to both triangles).

So,

$$\displaystyle \frac{WX}{XZ}=\frac{XY}{WX},\\ \displaystyle \frac{8}{XZ}=\frac{14}{8}.$$

$$\displaystyle XZ= \frac{64}{14}=\frac{32}{7},\\ \displaystyle YZ = 14 - \frac{32}{7}=\frac{98}{7}-\frac{32}{7}=\frac{66}{7} \approx9.42857.$$

Aug 2, 2020
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Thanks very much Tiggsy,

I have updated my pic to display what you have said.

https://www.geogebra.org/classic/c8gbdz5w

Melody  Aug 3, 2020
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Thank you everyone! I really needed some help on the question, and you helped me so much. Thank you!

Aug 3, 2020