Question

Find the length of UT.

Answer 1

Answer: A. 32

Concept:

Here, we need to know the idea of the intersecting chord theorem and segment addition postulate.

The intersecting chord theorem states that when two chords intersect at a point, P, the product of their respective partial segments is equal.

The Segment Addition Postulate 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:

Given information

CW = 12

TW = 14

VW = 2x + 5

UW = 2x + 2

Given expression deducted from intersecting chord theorem

CW · VW = TW · UW

Substitute values into the expression

(12) · (2x + 5) = (14) · (2x + 2)

Expand parentheses and apply the distributive property

24x + 60 = 28x + 28

Subtract 14x on both sides

24x + 60 - 24x = 28x + 28 - 24x

60 = 4x + 28

Subtract 28 on both sides

60 - 28 = 4x + 28 - 28

32 = 4x

Divide 4 on both sides

32 / 4 = 4x / 4

x = 8

Given expression deducted from the segment addition postulate

UT = UW + TW

Substitute values into the expression

UT = 2x + 2 + 14

Substitute x value into the expression

UT = 2 (8) + 2 + 14

UT = 16 + 2 + 14

Combine like terms

UT = 32

Hope this helps!! :)

Please let me know if you have any questions