Let  stand for the length of ; then the length of  is twice this, or . The figure referenced is below:

If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords - that is,

Substituting the appropriate quantities, then solving for :

This statement is identically true. Therefore, without further information, we cannot determine the value of  - the length of .

Let  stand for the length of ; then the length of   is . The figure referenced is below:

If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords - that is,

Substituting the appropriate quantities, then solving for :

This quadratic equation can be solved by completing the square; since the coefficient of  is 12, the square can be completed by adding

to both sides:

Restate the trinomial as the square of a binomial:

Take the square root of both sides:

 or  

Either

, 

in which case

,

or 

in which case

,

Since  is a length, we throw out the negative value; it follows that , the correct length of .

In a circle, a diameter perpendicular to a chord bisects the chord. This makes  the midpoint of ; consequently, .

The figure referenced is below:

If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords - that is,

Setting  , and solving for :

,

the correct length.

Let , in which case ; the figure referenced is below (not drawn to scale). 

If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords - that is,

Setting  , and solving for :

, 

which is the length of .

A diameter of a circle perpendicular to a chord bisects the chord. Therefore, the point of intersection  is the midpoint of , and

. 

Let  stand for the common length of  and ,

The figure referenced is below.

If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords - that is,

Set  and , and ; substitute and solve for :

This is the length of ; the length of  is twice this, so

The measure of the angle formed by the two secants to the circle from a point outside the circle is equal to half the difference of the two arcs they intercept; that is,

The ratio of the degree measure of  to that of  is that of their lengths, which is 7 to 2. Therefore,

Letting :

Therefore, in terms of :

Without further information, however, we cannot determine the value of  or that of . Therefore, the given information is insufficient.