Solution
We want to find the length |PO|
First notie that |PG| = |GO|
We are already given that
[tex]\begin{gathered} |PG|=-x+10 \\ |GO|=-3(x+2) \end{gathered}[/tex]
We will equate te above equations and solve for x
[tex]\begin{gathered} |PG|=|GO| \\ -x+10=-3x-6 \\ 3x-x=-6-10 \\ 2x=-16 \\ x=-\frac{16}{2} \\ x=-8 \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} |PG|=-x+10=-(-8)+10=18 \\ |GO|=-3(x+2)=-3(-8+2)=-3(-6)=18 \end{gathered}[/tex]
Therefrore, the length |PO| is
[tex]|PO|=18+18=36[/tex]
Therefore, the answer is Option A
