# Check my work? which statement is true?

Jun 9, 2018

The fourth one

#### Explanation:

If I understood correctly, this is the figure:

As you can see, $P A$, $P B$ and $A B$ 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 $A B$ lies and the radius $P A$ are perpendicular, and thus $P A B$ is a right triangle.

Jun 9, 2018

Answer should be 4($\angle$PAB is a right angle)

#### Explanation:

Dear hjjhk,
According to me,correct answer should be 4($\angle$PAB is a right angle).

• REASON:

The question states as-

Where, $\overline{P A}$ denotes the radius.
$\overline{A B}$ 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 $P A$ cannot be equal to $P B$.

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.