Chapter 4.7, Problem 13WE

To determine

To complete: the proof $PA=PC$ .

Explanation of Solution

Given information:

  $P$ is on the perpendicular bisector of $\overline{AB}$ .

  $P$ is on the perpendicular bisector of $\overline{BC}$ .

Given figure,

  

Calculation:

Since, $P$ is on the perpendicular bisector of $\overline{AB}$ ,

This implies that, $PA=PB$

And, $P$ is on the perpendicular bisector of $\overline{BC}$ , this gives $PB=PC$ .

Further, $PA=PB$ and $PB=PC$

Therefore, the result obtained is $PA=PC$ .