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

Refer to the redrawn figure below.

Because C is the centroid,
PZ = ZR; QY = YR; and PX = XQ.

Part a.
If CY = 10, then PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer:
PC = 20
PY = 30

Part b.
If QC = 10, then ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer:
ZC = 5
ZQ = 15

Part c.
Given: PX = 20.
Because the median bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:
PQ = 40