In a triangle ABC, P and Q are the mid points of AB and BC respectively. Point G and H l ie’s on AC such that they are

In a triangle ABC, P and Q are the mid points of AB and BC respectively. Point G and H l ie’s on AC such that they are the mid-point of PR and QR respectively. Here R is a point outside the triangle. Then what is the Ratio of area ∆ ABC : area ∆ PQR?

(a) 2 : 3

(b) 5 : 2

(c) 3 : 5

(d) 2 : 1

Sol:

∆ BPQ ~ ∆ BAC

AC = 2PQ

AC II PQ

BE = 2BD

BD = DE

∆ RGH ~∆ RPQ

PQ = 2GH

PQ II GH

RY = 2RX

⇒ RX = XY

Since

RX = XY = BD = DE

RY = BE = h

=2 : 1