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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
avatar+1322 
0

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 laugh 

 

*** 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
avatar+24 
0

I am not seeing any right triangle. Please put the asymptote code in an asymptote renderer like https://artofproblemsolving.com/texer/oqgvgvlb

aDumbDude  Jul 30, 2020
 #3
avatar+1128 
0

Here's the picture 

 Jul 30, 2020
 #4
avatar+24 
0

Thank you guys so much I got it! laugh

 Aug 3, 2020

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