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4. Assume that segments that appear to be tangent are tangent. Enter
the number only for your answer.
If PQ = 4x + 2, QR = 7x – 19, and QU = 34, find ST.
Your answer

10 points 4. Assume that segments that appear to be tangent are tangent. Enter the-example-1
User Rolfk
by
8.3k points

1 Answer

6 votes

Given:

The lengths PQ = 4x + 2, QR = 7x – 19, and QU = 34

We need to determine the value of ST.

Value of x:

By two tangent theorem, we have;

PQ = QR

Substituting the values, we get;


4x+2=7x-19


-3x+2=-19


-3x=-21


x=7

Thus, the value of x is 7.

Length of PQ and QR:

Substituting x = 7 in the expressions of PQ and QR, we get the lengths.

Length of PQ =
4(7)+2=28+2=30

Length of QR =
7(7)-19=49-19=30

Radius of the circle:

The radius of the circle PU can be determined using the Pythagorean theorem.

Thus, we have;


QU^2=PQ^2+PU^2

Substituting the values, we get;


34^2=30^2+PU^2


1156=900+PU^2


256=PU^2


16=PU

Thus, the radius of the circle is 16.

Length of ST:

The length of ST is
ST=SU+UT

Substituting SU = UT = 16 because the radius of the circle is 16.

Thus, we have;


ST=16+16


ST=32

Thus, the length of ST is 32.

User Thiago Souza
by
8.9k points
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