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# Help!!!!

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Triangle WXY has side lengths XY=14 and WX=8 . The tangent to the circumcircle of triangle WXY at X is drawn, and the line through W that is parallel to this tangent intersects XY at Z. Find YZ.

Thank you so much!!!

Noori

Aug 2, 2020

#1
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By similar triangles, YZ = 23/4.

Aug 2, 2020
#2
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Its always a good idea to search your problem before you post it.

A lot of problems have already been answered so there is no point in posting it here.

Aug 2, 2020
#3
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Both answers are incorrect. Thanks for trying to help!

Noori  Aug 2, 2020
#4
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Hmm Alright.  Sorry that I wasn't able to help

qwertyzz  Aug 2, 2020
#5
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Let a triangle WXY be a right-angled triangle.

XY = 14            WX = 8

tan(Y) = 8 / 14        ∠Y  =  ∠XWZ  = 29.7448813°

XZ = tan(XWZ) * WX = 4.571428571

YZ = XY - XZ = 9.428571429 ( This is the correct answer!!! Believe me. )

Guest Aug 2, 2020
#6
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How do you know that both of those answers are incorrect? What's the correct answer, then???

Guest Aug 2, 2020
#7
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Is this rounded? If so, could you please give the exact answer?---------> for post 5

Noori  Aug 2, 2020
edited by Noori  Aug 2, 2020
#8
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I don't know, that is why I still haven't said I got the answer.

Noori  Aug 2, 2020
#9
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This only works in a right triangle.

Noori  Aug 2, 2020
#10
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Diagram: Aug 2, 2020
#11
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It would help if there were not two threads running for this question.

There is another thread which does contain the correct solution and the correct answer, 66/7.

#5 above should be disregarded, it considers only the specific case where WY is a diameter of the circle.

WY is parallel to the tangent a X, it needn't be the diameter.

Aug 3, 2020