Question

# Point P is inside △ 𝐴𝐵𝐶 and is equidistant from points A and B. On which of the following segments must P be located?

- AB
- The perpendicular bisector of AB
- The perpendicular bisector of AC
- The midsegment opposite AB

Hint:

- Perpendicular bisector theorem
- According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.

## The correct answer is: The perpendicular bisector of AB

### Answer:

- Step by step explanation:
- Given:

Point P is inside △ 𝐴𝐵𝐶 and is equidistant from points A and B.

- Step 1:
- In △ ABC,

According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.

So,

As P is equidistant from A and B it lies on perpendicular bisector on AB.

- Final Answer:

Correct option. B. The perpendicular bisector of 𝐴𝐵.

- Given:

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