Since  is equilateral, the length of chord  is equivalent to the length of , and, subsequently, the radius of the circle. If Statement 1 alone is assumed, the radius of the circle can be calculated using the area formula.

If Statement 2 alone is assumed, the length of  is one third of the known perimeter.

For two chords in the same circle to be congruent, it is necessary and sufficient that their arcs have the same length.

By arc addition, the length of  is the sum of the lengths of  and , which we will call  and , respectively. Similarly, the length of  is the sum of the lengths of  and , which we will call  and , respectively.

If Statement 1 alone is assumed, 

Subsequently, 

,

so  is longer than . The arcs are of unequal length so their chords are as well. This makes Statement 1 sufficient to answer the question. A similar argument can be made that Statement 2 alone answers the question.

Statement 1 only gives information about two other chords, whose relationship with the first two is not known. Statement 2 only gives the congruence of two inscribed angles - and, subsequently, since congruent inscribed angles intercept congruent arcs, that  - but gives no information about the individual sides.

Assume both statements.

Congruent chords of the same circle must have arcs of the same degree measure, so, from Statement 1, since , then . From Statement 2, as stated before, . Then,

By arc addition, this statement becomes

.

Since congruent chords on the same circle have congruent arcs, 

.

Congruent chords of the same circle must have arcs of the same degree measure, so

 if and only if . 

Assume both statements. Then , since, in the same circle, congruent arcs have congruent chords, it follows from Statement 1 that 

.

Also, since congruent inscribed angles intercept congruent arcs, it follows from Statement 2 that 

By arc addition,

can be expressed as 

.

Examples of the values of the four arc measures , , , and  can easily be found to make  and  so that 

 is either true or false; consequently,  may be true or false.

The two statements together are insufficient.

If two chords of a circle intersect inside it, and two more chords are constructed connecting endpoints, as is the case here, the resulting triangles are similar - that is, 

 if and only if the triangles are congruent. From either statement alone, we are given a side congruence - from Statement 1 alone it follows that , and from Statement 2 alone, it follows that . Either way, the resulting side congruency, along with two angle congruencies following from the similarity of the triangles, prove by way of the Angle-Sude-Angle Postulate that , and, subsequently, that .

For two chords in the same circle to be congruent, it is necessary and sufficient that their minor arcs have the same length. Statement 1 asserts this, so it is sufficient to answer the question.

It is also necessary and sufficient that their major arcs have the same degree measure. Statement 2 alone asserts this, so it is sufficient to answer the question.

Since only positive numbers have logarithms, the expression  must be positive, so

Therefore, the vertical asymptote must be the vertical line of the equation

.

In order to determine which side of the -axis the vertical asymptote falls, it is necessary to find the sign of  ; if it is negative, it is on the left side, if it is positive, it is on the right side.

Assume both statements are true. By Statement 1,  is positive. If  is positive, then  is negative, and vice versa. However, Statement 2, which mentions , does not give its actual sign - just the fact that its sign is the opposite of that of , which we are not given either. The two statements therefore give insufficient information.

Since a logarithm of a nonpositive number cannot be taken, 

Therefore, the vertical asymptote must be the vertical line of the equation

.

Each of Statement 1 and Statement 2 gives us only one of  and . However, the two together tell us that 

making the vertical asymptote

.

Only positive numbers have logarithms, so:

Therefore, the vertical asymptote must be the vertical line of the equation

.

In order to determine which side of the -axis the vertical asymptote falls, it is necessary to find out whether the signs of   and  are the same or different. If  and  are of the same sign, then their quotient  is positive, and  is negative, putting  on the left side of the -axis. If  and  are of different sign, then their quotient  is negative, and  is positive, putting   on the right side of the -axis. 

Statement 1 alone does not give us enough information to determine whether  and  have different signs. , for example, but , also.

From Statement 2, since the product of  and  is negative, they must be of different sign. Therefore,  is positive, and  falls to the right of the -axis.

Only positive numbers have logarithms, so:

Therefore, the vertical asymptote must be the vertical line of the equation

.

Statement 1 alone gives that .  is the reciprocal of this, or , and , so the vertical asymptote is .

Statement 2 alone gives no clue about either , , or their relationship.