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Answer: A. 32
Concept:
Here, we need to know the idea of the intersecting chord theorem and segment addition postulate.
The<u> intersecting chord theorem </u>states that when two chords intersect at a point, P, the product of their respective partial segments is equal.
The<u> Segment Addition Postulate</u> states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
<u>Given information</u>
CW = 12
TW = 14
VW = 2x + 5
UW = 2x + 2
<u>Given expression deducted from intersecting chord theorem</u>
CW · VW = TW · UW
<u>Substitute values into the expression</u>
(12) · (2x + 5) = (14) · (2x + 2)
<u>Expand parentheses and apply the distributive property</u>
24x + 60 = 28x + 28
<u>Subtract 14x on both sides</u>
24x + 60 - 24x = 28x + 28 - 24x
60 = 4x + 28
<u>Subtract 28 on both sides</u>
60 - 28 = 4x + 28 - 28
32 = 4x
<u>Divide 4 on both sides</u>
32 / 4 = 4x / 4
x = 8
<u>Given expression deducted from the segment addition postulate</u>
UT = UW + TW
<u>Substitute values into the expression</u>
UT = 2x + 2 + 14
<u>Substitute x value into the expression</u>
UT = 2 (8) + 2 + 14
UT = 16 + 2 + 14
<u>Combine like terms</u>
UT = 32
Hope this helps!! :)
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