Statement 2 is unhelpfful as it gives no information about the circles - only a triangle which is not given in that statement to have any connection to the circles. Statement 1 alone is unhelpful in that it only identifies two sides of a triangle as  diameters of the circles without giving their lengths.

Now assume both statements to be true. The hypotenuse of a right triangle, which Statement 2 gives as , must be the longest side, so  has greater length than . This means that the circle with  as a diameter, Circle 1, must have a greater diameter than one with  as a diameter, Circle 2. Since Circle 1 has the greater diameter, it has the greater radius.

Statement 1 alone yields insufficient information, since, as seen in the diagram below, the circles that circumscribe a square and a triangle with the same sidelength have different sizes:

Statement 2 is insufficient since it gives no hints about the size of the hexagon.

Assume both statements. The six radii of a regular hexagon divide it into six equilateral triangles, by symmetry; therefore, the radius of a regular hexagon is equal to its sidelength, which is given in Statement 1 as 10. Since the radius of a regular hexagon is equal to that of the circle in which it is inscribed, the circle has radius 10.

This can be seen by examining the figure below:

Let  be the measure of  and  be radius.

From Statement 1 alone, the area of the shaded sector is 

However, we have no other information, so we cannot determine the value of the radius.

From Statement 1 alone, the length of the arc of the shaded sector  is

Again, we have no other information, so we cannot determine the value of the radius.

Assume both statements hold. From Statements 1 and 2, we have, respectively,

and

If we divide, we get the radius:

.

The actual form of the equation of a circle is 

,

where  is the location of the center, and  is the radius. 

The radius of the circle in the equation

is therefore . We need to know the value of  in the equation.

Assume both statements are true. Then we can add the equations to get :

But without further information, we cannot determine .

If a right triangle is inscribed inside a circle, the hypotenuse of the triangle is a diameter of the circle; therefore, its length is the diameter, and half this is the radius. However, each statement alone gives us the length of only one side, and does not clue us in to which side is the hypotenuse.

Assume both statements are true, however. The hypotenuse must always be the longest side of the right triangle, so if two sides have the same length, they must be the legs. A right triangle with congruent legs is a 45-45-90 triangle, and by the 45-45-90 Theorem, its hypotenuse must measure  the length of a leg. Since each leg of  measures 100, the length of the hypotenuse, and the diameter of the circle, are , and the radius is half this, or .

The diameter of a circle with an inscribed rectangle is equal to the length of the diagonal of the rectangle; once this diameter is found, it can be divided by 2 to yield the radius.

Statement 1 alone gives this length, from which the radius can be found to be . Statement 2 alone gives only the length of one set of opposite sides, from which the length of the diagonal cannot be determined.

If a right triangle is inscribed inside a circle, the hypotenuse of the triangle is a diameter of the circle; therefore, its length is the diameter, and half this is the radius.

Assume Statement 1 alone. The area of a right triangle is half the product of the lengths of the legs, which is 36. However, this is not enough to determine the length of the hypotenuse. 

For example, if the legs measure 8 and 9, the triangle has area

By the Pythagorean Theorem, the hypotenuse measures

,

which is the diameter of the circle; half this, or , is the radius of the circle.

If the legs measure 6 and 12, the triangle has area

By the Pythagorean Theorem, the hypotenuse measures

,

which is the diameter of the circle; half this, or , is the radius of the circle.

Therefore, Statement 1 is inisufficient to give the radius.

Assume Statement 2 alone. The hyppotenuse of a right triangle must be longer than either leg, so it is impossible for either of the two equally long sides  and  to be the hypotenuse of ; they must be its legs. Since the legs are of the same length,  is a 45-45-90 triangle, and by the 45-45-90 Theorem, hypotenuse  has length  that  of a leg, or . This is the diameter of the circle, and the radius is half this, or 

The actual form of the equation of a circle is 

,

where  is the location of the center, and  is the radius. 

The radius of the circle in the equation

is therefore , making Statement 2 alone sufficient to answer the question - and Statement 1 unhelpful.

Assume both statements are true. Since we have no way to determine which, if either, of the legs of  is the longer, we have no way to compare the diameters, and, consequently, no way to compare the radii, of the circles with those segments as diameters.

If a right triangle is inscribed inside a circle, the hypotenuse of the triangle is a diameter of the circle; therefore, its length is the diameter, and half this is the radius. However, from the two statements, it cannot be determined which segment is the hypotenuse. 

If   is the hypotenuse, then the radius is half its length; since , the radius is 10.

If  is the hypotenuse, then, since the hypotenuse is the longest side of a right triangle,  - that is, . The radius is greater than 10.

Therefore, the radius depends on which side is the hypotenuse; since that is not clear, the radius cannot be determined.