Check my work? which statement is true?

enter image source here

2 Answers
Jun 9, 2018

The fourth one

Explanation:

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.

Jun 9, 2018

Answer should be 4(/_PAB is a right angle)

Explanation:

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

  • REASON:

The question states as-
enter image source here
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.