Question

In triangle PQR, C is the centroid.

A. If CY = 10, find PC and PY
B. If QC = 10, find ZC and ZQ
C. If PX = 20, find PQ

Answer 1

Because point C is the centroid of the triangle, therefore:

Segments PZ = ZR; RY = YQ; QX = XP

A.
If CY = 10, then

PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answers:

PC = 20

PY = 30

B.
If QC = 10, then

ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answers:

ZC = 5

ZQ = 15

C.
If PX = 20
because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:

PQ = 40