Question

ANGLES, ARCS, AND SEGMENTS FORMED BY INTERSECTING CHORDS, SECANTS, AND TANGENTS.

Answer 1

Explanation

We are given the following information from the figure:

`\begin{gathered} |QP|=x \\ |RQ|=12 \\ |RS|=18 \\ |ST|=16 \end{gathered}`

We are to determine the value of x. This can be achieved by using the formula below:

`\begin{gathered} |RQ|\cdot|RP|=|RS|\cdot|RT| \\ where \\ |RP|=|RQ|+|QP| \\ |RT|=|RS|+|ST| \end{gathered}`

Using the formula above and substituting their corresponding values, we have:

`\begin{gathered} 12(12+x)=18(18+16) \\ 12(12+x)=18(34) \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }12 \\ (12(12+x))/(12)=(18(34))/(12) \\ 12+x=51 \\ x=51-12 \\ x=39 \end{gathered}`

Hence, the value of |PQ| is 39.