Question

C is the circumcenter of PQR
PC=3x+7, RC=5x-15 and QC=51-x.
what does RC equal?

Answer 1

40

Explanation:

Answer 2

`RC = 40`

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,

`PC = RC = QC`

Let's find the value of x using:

`PC = RC`

`3x + 7 = 5x - 15` (substitution)

Collect like terms

`3x - 5x = -7 - 15`

`-2x = -22`

Divide both sides by -2

`x = (-22)/(-2)`

`x = 11`

Find the measure of RC

`RC = 5x - 15`

substitute x = 11 into the equation

`RC = 5(11) - 15`

`RC = 55 - 15`

`RC = 40`