in the accompanying diagram of circle O,chords AB and CD intersect at E. If AE=3,EB=4,CE=x, and ED=x-4,what is the value

To find the value of x, we can use the property of intersecting chords in a circle.

According to the property, when two chords intersect inside a circle, the products of their segments are equal.

So, in this case, we have AE × EB = CE × ED.

Given AE = 3 and EB = 4, we can substitute these values:

3 × 4 = CE × (x-4)

12 = CE × (x-4)

Now, we have an equation we can solve for x.

To do this, we can expand the right side:

12 = CE × x - 4CE

Next, let's gather the x terms on one side and the constant terms on the other side:

CE × x = 4CE + 12

Now, we can factor out CE on the right side:

CE × x = CE × (4 + 12/CE)

Dividing both sides of the equation by CE, we get:

x = 4 + 12/CE

So, the value of x is 4 plus 12 divided by CE.