Question 190350
Let ED = x.
Then CE = 2x + 2
According to the chord segment theorem in geometry, (CE)(DE)=(AE)(BE)
By substitution, we have
{{{(2x+2)x=6*10}}}
Simplifying, we get
{{{2(x+1)x=6*10}}}
{{{(x+1)x=30}}}  dividing both sides by 2

Re-write it in standard form, we have:
{{{x^2+x-30=0}}}
Solving for x, we have
{{{(x-5)(x+6)=0}}}
So x = 5 or x= -6 (reject this negative number)
Thus DE = 5. Therefore CE =2x + 2 = 12.