10 points
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

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;

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 =

Length of QR =

Radius of the circle:

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

Thus, we have;

Substituting the values, we get;

Thus, the radius of the circle is 16.

Length of ST:

The length of ST is

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

Thus, we have;

Thus, the length of ST is 32.

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step-by-step explanation: