Use the tangent-secant theorem:
If a secant is drawn from an external point, the product of the secant and the external secant equals the square of the tangent.
This means, when applied to this problem,
ED*EC=EA*EB=(ET)^2, where ET is tangent to circle drawn from E.
Here, we only need the first part of the equation, without the use of ET.
Thus
ED*EC=EA*EB ......................(1)
ED=1+x+4=x+5
EC=x+4
EA=11+x+1=x+12
EB=x+1
Substitute values into (1)
(x+5)(x+4)=(x+12)(x+1)
Expand both sides
x^2+9x+20 = x^2+13x+12
subtract x^2 from both sides and solve for x
9x+20=13x+12
4x=20-12=8
x=8/4=2
Check:
(x+4)(x+5)=(6)(7)=42,
(x+12)(x+1)=14*3=42, so checks.
Answer: x=2
