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# I need 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.

Asymptote code:

[asy]
unitsize(2 cm);

pair A, B, C, D;

A = dir(110);
B = dir(210);
C = dir(330);
D = extension(B, C, A, A + rotate(90)*(B));

draw(Circle((0,0),1));
draw(A--B--C--cycle);
draw((B + rotate(90)*(B))--(B - rotate(90)*(B)));
draw(A--(A + 2.2*(rotate(90)*(B))));

label("\$W\$", A, N);
label("\$X\$", B, SW);
label("\$Y\$", C, SE);
label("\$Z\$", D, SW);
[/asy]

Thanks. I would not like the answer, I would like a solution, because I would really want to understand.

Jul 30, 2020

#1
+1421
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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.

Hint:::    Use the right-angled triangle with legs of 8 and 14

*** No matter what type of a triangle is used, the result will be the same!!! ***

Jul 30, 2020
edited by Dragan  Jul 30, 2020
edited by Dragan  Jul 31, 2020
edited by Dragan  Jul 31, 2020
#2
+41
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I am not seeing any right triangle. Please put the asymptote code in an asymptote renderer like https://artofproblemsolving.com/texer/oqgvgvlb

#3
+1154
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Here's the picture

Jul 30, 2020
#4
+41
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Thank you guys so much I got it!

Aug 3, 2020