![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](https://www.gkseries.com/blog/wp-content/uploads/2024/04/In-a-triangle-ABC-P-and-Q-are-the-mid-points-of-AB-and-BC-respectively.-Point-G-and-H-l-ies-on-AC-such-that-they-are.jpg)
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:
![](https://www.gkseries.com/blog/wp-content/uploads/2024/04/image-42-1024x833.png)
∆ 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
![](https://www.gkseries.com/blog/wp-content/uploads/2024/04/image-43-1024x899.png)
=2 : 1