To answer this question, we need to know that if two chords intersect inside a circle, we have that the product of the lengths of each segment in one chord is equal to the product of the segments in the other chord. That is, this is the formula for intersecting chords. That is:
[tex]x\cdot10=6\cdot5[/tex]
Then, solving for x, we have:
[tex]x\cdot10=30\Rightarrow(x\cdot10)\Rightarrow\frac{(x\cdot10)}{10}=\frac{30}{10}\Rightarrow x=3[/tex]
Therefore, the value for x is 3, or x = 3.
