Question

Find the measure of the line segment RQ​

Answer 1

Answer: RQ = 48

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Work Shown:

RS*QS = (TS)^2

RS*(QR+RS) = (TS)^2

27*(5x-12+27) = (45)^2

27*(5x+15) = 2025

135x+405 = 2025

135x = 2025-405

135x = 1620

x = 1620/135

x = 12

Use this to find the length of QR, which is the same as RQ

QR = 5x-12

QR = 5*12-12

QR = 60-12

QR = 48

Answer 2

9514 1404 393

Answer:

RQ = 48

Explanation:

The product of secant segment lengths to the points of intersection with the circle is the same for both secants. The tangent is a degenerate case where the two points of intersection are the same.

ST·ST = SR·SQ

SQ = ST^2/SR = 45^2/27 = 75

RQ = SQ -SR = 75 -27

RQ = 48