Answer: [tex]x=\frac{8}{3}[/tex]
Step-by-step explanation:
By the Intersecting secants theorem, we know that:
[tex]EC*ED=EB*EA[/tex]
Then, substituting, we get:
[tex](x+4)(x+4+1)=(x+1)(x+1+11)\\\\(x+4)(x+5)=(x+1)(x+12)[/tex]
Now we need to expand the expression:
[tex]x^2+5x+4x+20=x^2+12x+x+12[/tex]
Simplifying, we get that the value of "x" is:
[tex]x^2+9x+20=x^2+12x+12\\\\9x+20=12x+12\\\\20-12=12x-9x\\\\8=3x\\\\x=\frac{8}{3}[/tex]
