Answer:
PC=40 units
Step-by-step explanation:
we know that
The circumcenter is the center of the triangle's circumcircle (the circle that passes through all three of the triangle's vertices)
That means
PC=RC=QC----> is the radius of the circumcircle
step 1
Find the value of x
equate PC and RC
[tex]3x+7=5x-15[/tex]
solve for x
[tex]5x-3x=7+15\\2x=22\\x=11[/tex]
Verify
substitute the value of x
[tex]PC=3x+7=3(11)+7=40\ units[/tex]
[tex]RC=5x-15=5(11)-15=40\ units[/tex]
[tex]QC=51-x=51-11=40\ units[/tex]
so
[tex]PC=RC=QC[/tex] ----> is ok
