Question

Given the circle below with secant SRQ‾SRQ and tangent PQ‾PQ , find the length of SR‾SR . Round to the nearest tenth if necessary

Answer 1

Given,

The measure of PQ is 24.

The measure of RQ is 17.

Required:

The measure of SR.

If a secant and tangent are drawn to a circle from the same external point, the product of length of the secant and its external segment equal the square of the length of the tangent segment.

`\begin{gathered} SQ* QR=PQ^2 \\ (SR+RQ)* QR=PQ^2 \\ (SR+17)*17=24^2 \\ 17SR+289=576 \\ 17SR=287 \\ SR=16.9 \end{gathered}`

Hence, the value of SR is 16.9