Chapter 9.5, Problem 28WE

To determine

To Prove: $PA=PB+PC$ with the help of Ptolemy's theorem.

Explanation of Solution

Given information:

Equilateral $△ABC$ is inscribed in a circle.

  $P$ is any point $\stackrel{⌢}{BC}$

Consider the following figure:

  

By Ptolemy's theorem,

  $PB·AC+PC·AB=PA·BC$

Since the triangle is equilateral, hence $AC=AB=BC$ .

Therefore, it is conclude that $PA=PB+PC.$