Help on circles problem

[JSZ2005]

Hi i have a question about this problem, i think it is correct but the practice thing says i'm wrong

Here is my thinking:
A theorem says that from a given point and circle the products of the two lengths of the two segments from the point to the circle is constant.
So in this case 3*6 = 2*x and solving I got 9 for the length AX
Then I used the triangle inequality theorem which says that for triangle AXP the third side length AP is less than 16 (9+3+4)
according to that, the length of segment AP could be less than AX but it doesn't specify anything else so i assumed that it was larger than AX
But the correct answer was Column B is greater

Anyone have any clue?

 

[Denis]

Why are the "choices" so "confusing"?
Is this not sufficient:
1: AP > AX
2: AP < AX
3: AP = AX
4: More info required

 

[mmm4444bot]

Why are the "choices" so "confusing"? …

You understand their meaning. The reason for setting up a presentation like that could be so that the machine can create different exercises (eg: change parameters) without having to reword the multiple choices each time.

What I find confusing is the OP's first theorem statement.

?

 

[Dr.Peterson]

Here is my thinking:
A theorem says that from a given point and circle the products of the two lengths of the two segments from the point to the circle is constant.
So in this case 3*6 = 2*x and solving I got 9 for the length AX
Then I used the triangle inequality theorem which says that for triangle AXP the third side length AP is less than 16 (9+3+4)
according to that, the length of segment AP could be less than AX but it doesn't specify anything else so i assumed that it was larger than AX
But the correct answer was Column B is greater

Anyone have any clue?

Assuming won't work; if an inequality you try is inconclusive, you need to do something else.

Try applying a different case of the same theorem: Just as you used XQ*XZ = XY*XA (focusing on point X), try doing the same with point P.

To be more specific, you used the first case shown here; use the second.