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larisa86 [58]
3 years ago
15

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

Mathematics
1 answer:
Readme [11.4K]3 years ago
8 0

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.

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