We know that
BP and EC are perpendicular bisectors. This means they form a 90° angle at the intersection points B and C, also, the equally divide segments AC and BD.
Now, to find PC, first, we need to find segment BC in order to use Pythagorean's theorem.
We know that AD=45, and it's also formed by the sum of segments AB, BC, and CD, which are all the same, that's why we are going to call them x.
[tex]AD=3x=45\rightarrow x=\frac{45}{3}=15[/tex]
This means segment BC is equal to 15 centimeters.
Now, we can use Pythagorean's theorem to find BP which is a leg of triangle PCB
[tex]PC^2=BC^2+BP^2[/tex]
But, BP=8 and BC=15, so
[tex]PC=\sqrt{15^2+8^2}=\sqrt[2]{225+64}=\sqrt{289}=17\operatorname{cm}[/tex]
Therefore, segment PC is 15 centimeters long.
