Check my work? which statement is true?

If I understood correctly, this is the figure:

As you can see, #PA#, #PB# and #AB# have all different lengths, so answer #2# and #3# are wrong.

In general, we know that everytime you draw a tangent line to a circle, and the line intersects the circle in a certain point #A#, then the line and the radius passing through #A# will be perpendicular.

So, in this case, the line in which #AB# lies and the radius #PA# are perpendicular, and thus #PAB# is a right triangle.

Dear hjjhk,
According to me,correct answer should be 4(#/_#PAB is a right angle).

• REASON:

The question states as-

Where, #bar(PA)# denotes the radius.
#bar(AB)# denotes the tangent to the circle.
The a Radius Perpendicular Theorem states, Radius is always perpendicular to the tangent.

1. Option 1:
   Option 1 is impossible as it is always right angle.

2. Option 2:
   Option 2 is not correct in any sense because point #B# lies out of the circle as tangent is drawn to the circle. So, radius #PA# cannot be equal to #PB#.

3. Option 3:
   Option 3 may be correct in limiting case but it is not always correct.

4. Option 4:
   Option 4 must be correct because Radius is always perpendicular to the tangent.