Theorem: If two chords intersect within a circle, then the product of the lengths of the segments (parts) of one chord is equal to the product of the lengths of the segments of the other chord.
This means that
[tex]PA\cdot PC=PB\cdot PD.[/tex]
If PA=PB, then subtituting PA instead of PB in previous equality you get
[tex]PA\cdot PC=PA\cdot PD|:PA\Rightarrow PC=PD.[/tex]
Answer: true.
