In triangle POR C is the centroid a If CY 10 find PC and PY

In triangle POR, 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

Solution

Centroid divides line joining midpoint of a line to opposite vertex in the ratio of 2:1

Using that knowledge, we have :

a.

PC = 2CY, so, PC = 2*10 = 20
PY = CY+PC = 20+10 = 30

b.

QC = 10
Therefore, 2CZ = QC, So, CZ = QC/2 = 5
ZQ = ZC+QC = 5+10= 15

c. PX = 20
We know that XR is line passing thorugh centroid and meeting R( the vertex opposite to it)
Therefore, X is midpoint of PQ
So, PQ = PX+XQ, since XQ = PX
we have PQ = PX+PX = 2*PX = 40
PQ = 40