Given:
Length of chords of one segment = 11 and 8
Length of chords of other segment = 2 and x
To find:
The value of x.
Solution:
If two chords intersect each other inside a circle, the products of length their segments are equal.
[tex]\Rightarrow a \cdot b =c \cdot d[/tex]
[tex]\Rightarrow 11 \cdot 8 =2 \cdot x[/tex]
[tex]\Rightarrow 88 =2x[/tex]
Divide by 2 on both sides.
[tex]$\Rightarrow\frac{88}{2} =\frac{2x}{2}[/tex]
[tex]$\Rightarrow 44 =x[/tex]
Switch the sides.
[tex]$\Rightarrow x=44[/tex]
The value of x is 44.