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.

aDumbDude Jul 30, 2020

#1**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

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

Dragan Jul 30, 2020