Question

in ∆abc bc=ab and ∠abc=90°. p is the midpoint of BC.PQ |_AC at Q. then prove that ar(∆ABC) =8ar(∆PQC)​

Answer 1

Answer:

Given:  In ∆ABC, P is the mid point of BC. PQ||CA, PQ meets AB in Q. QR||BC, QR meets AP  in R.

To prove: 1.  AP = 2 AR

  2. BC = 4 QR

Proof:

 In ∆ABC, P is the mid point of BC and PQ||AB.

∴ Q is the mid point of AB  (Converse of mid-point theorem)

 

In ∴ ABP, Q is the mid point of AB and QR||BP.

∴ R is the mid point of AP.  (Converse of mid point theorem)

⇒ AP = 2AR

 

In ∆ABP, Q is the mid point of AB and R is the mid point of AP.