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in the figure below, two chords intersect inside the circle at point V. suppose that VN = 22.5, VJ = 9, and VM = 18. Find JK.

In The Figure Below Two Chords Intersect Inside The Circle At Point V Suppose That VN 225 VJ 9 And VM 18 Find JK class=

Sagot :

To solve this problem we have to use the intersecting chords theorem which states a proportion between the four resulting segments,

Based on this theorem, we can define the following proportion

[tex]VM\times VN=KV\times VJ[/tex]

First, we find VK. We have to replace the given information

[tex]\begin{gathered} 18\times22.5=KV\times9 \\ KV=\frac{405}{9}=45 \end{gathered}[/tex]

Now, by the sum of segments, we define an equation for JK.

[tex]\begin{gathered} JK=VJ+KV \\ JK=9+45=54 \end{gathered}[/tex]

Therefore, the chord JK is 54 units long.

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