Question

P,Q and R are midpoints of BC,CA and AB respectively of triangle ABC.PR and BQ meet at X.CR and PQ meet at Y.Prove that XY =1/4BC.​

Answer 1

Step-by-step explanation:

In a triangle line joining mid - point of two sides are parallel and half of third side 

PQ∥ABPQ=21AB→(i)QR∥BCQR=21BC→(ii)PR∥ACPQ=21AC→(iii)fromequation(i)(ii)

two pairs are parallel so, BPQR is a parallelogram

BP=QR=2BC→(iv)

In parallelogram diagonals bisects each other so

X is mid -point to PR. Similarly,

Y is mid- point on  QP

InΔRPQXY=21QRXY=21(21BC)41BC