The diagram shows a triangle bisected by a perpendicular bisector RC. This means the angle PCQ has been divided into two equal halves which are;
[tex]\angle PCR\text{ and }\angle QCR[/tex]
Note also that triangle PRC and triangle QRC both have the line segment RC in common.
Then if the line segment RC is a perpendicular bisector of line PQ, it means line segment PR equals RQ.
Therefore, in both triangles PRC and QRC, there is a congruence;
[tex]\begin{gathered} PR=RQ \\ RC=RC \\ \angle PCR=\angle QCR \end{gathered}[/tex]
Hence, line PC equals line QC.
We can now et up the following equation.
[tex]\begin{gathered} PC=QC \\ 3x-2=10 \\ \text{Add 2 to both sides;} \\ 3x-2+2=10+2 \\ 3x=12 \\ \text{Divide both sides by 3;} \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]
ANSWER;
x = 4
The correct answer is option C
