Question

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

Answer 1

Given:

C is the circumcenter of ΔPQR

PC = 3x + 7

RC = 5x - 15

QC = 51 - x

To find:

QC

Solution:

All vertices or a triangle are equidistant from its circumcenter.

$P C=R C=Q C$

Let us take $R C=Q C$.

$5 x-15=51-x$

Add 15 on both sides.

$5 x-15+15=51-x+15$

$5 x=66-x$

Add x on both sides.

$5 x+x=66-x+x$

$6 x=66$

Divide by 6 on both sides, we get

x = 11

Substitute x = 11 in QC.

QC = 51 - 11

      = 40

Therefore QC = 40.