The problem can be solved using the Power of a Point, which states that:
[tex]EC \cdot ED=EB \cdot EA[/tex].
Substituting
[tex]EC=x+4; ED=x+5; EB=x+1; EA=x+12,[/tex]
we have the equation
[tex](x+4) \cdot (x+5)=(x+1) \cdot (x+12)[/tex].
Expanding both sides we get,
[tex]x^2+9x+20=x^2+13x+12.[/tex]
Subtracting [tex]x^2[/tex] from both sides, we have
[tex]9x+20=13x+12[/tex].
Collecting x's and the numbers on two different sides, we have:
4x=8, which finally yields x=2.
Answer: x=2
