Question

With the two chords intersecting inside the circle, what is the length of the segment labeled with an x inside the circle?

Answer 1

Consider the following diaagram,

Given that side PD is 26 units,

$\begin{gathered} PD=26 \\ PC+CD=26 \\ 14+CD=26 \\ CD=12 \end{gathered}$

According to the Intersecting Secants Theorem,

$PB\times AP=PC\times PD$

Substitute the values and solve for 'x' as follows,

$\begin{gathered} 12\times(x+12)=14\times26 \\ 12x+144=364 \\ 12x=364-144 \\ 12x=220 \\ x=\frac{220}{12} \\ x\approx18.33 \end{gathered}$

Thus, the value of 'x' is approximately 18.33 units .