Answer:
[tex] RC = 40 [/tex]
Step-by-step explanation:
Given:
PC = 3x + 7,
RC = 5x - 15,
QC = 51 - x.
Required:
measure of RC
SOLUTION:
Given that C is the circumcenter of ∆PQR, therefore, vertices P, Q, and R are equidistant from C.
So therefore,
[tex] PC = RC = QC [/tex]
Let's find the value of x using:
[tex] PC = RC [/tex]
[tex] 3x + 7 = 5x - 15 [/tex] (substitution)
Collect like terms
[tex] 3x - 5x = -7 - 15 [/tex]
[tex] -2x = -22 [/tex]
Divide both sides by -2
[tex] x = \frac{-22}{-2} [/tex]
[tex] x = 11 [/tex]
Find the measure of RC
[tex] RC = 5x - 15 [/tex]
substitute x = 11 into the equation
[tex] RC = 5(11) - 15 [/tex]
[tex] RC = 55 - 15 [/tex]
[tex] RC = 40 [/tex]
