# where perpendicular bisectors intersect

- Author:
- Arthur Lee

We may use this applet to explore and explain the following property.

**For a triangle ABC, if two of its perpendicular bisectors intersect at a point P, this point should also lie on the third perpendicular bisector.**You may try the following steps to explore the figure.

- Click the check box to show a movable point Q and the segments connecting it with A, B and C.
- What happens when Q lies on the perpendicular bisector of AB?
- What happens when Q lies on the perpendicular bisector of AC?
- What would you expect to see if Q is moved to P? Why?

Go ahead to move Q and check. Write down your observation here.

Whenever BQ=CQ, Q should lie on the perpendicular bisector of BC. (If needed, move Q to some possible positions and check.) Do you know why?

Explain why you are sure P is one of those points equally far away from B and C (that means BP=CP).

So, can you conclude that P must lie on the perpendicular bisector of BC?