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Chords $\overline{WY}$ and $\overline{XZ}$ of a circle are perpendicular. If $XV = 4$, $WV = 3$, and $VZ = 9$, then find $YZ$.

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Chords $\overline{WY}$ and $\overline{XZ}$ of a circle are perpendicular. If $XV = 4$, $WV = 3$, and $VZ = 9$, then find $YZ$.

Sep 9, 2017

#1
+98141
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By the theory of intersecting chords.....

XV * ZV  =  WV * YV     ....so....

4 * 9  =  3 * YV       divide both sides by 3

[ 4 * 9 ]  / 3  =   YV

36 / 3  =  YV   =  12

And since the chords are perpendicular, by the Pythagorean Theorem.......

ZV^2 + YV^2  = YZ^2

9^2  +  12^2 = YZ^2

225   =  YZ^2        take the square root of both sides

15  =  YZ

Sep 9, 2017