Given:
[tex]\begin{gathered} AP=5 \\ \\ PD=8 \\ \\ CP=4 \end{gathered}[/tex]Find-:
The value of length PB
Explanation-:
The length of PB is:
When two chords intersect inside a circle, then the measures of the segments of each chord multiplied by each other are equal to the product from the other chord:
So, the value of PB is:
The applied property for the given circle is:
[tex]AD\cdot PD=CB\cdot PB[/tex]Then the value of PB is:
[tex]PB=\frac{AD\cdot PD}{CB}[/tex][tex]\begin{gathered} PB=\frac{(AP+PD)(PD)}{CB} \\ \\ PB=\frac{(5+8)(8)}{4+PB} \\ \\ PB(4+PB)=104 \\ \\ PB=8.3\text{ and }PB=-12.39 \end{gathered}[/tex]The length negative is not possible so, the value of PB is:
[tex]PB\approx8[/tex]
