Question

in triangle abc. p is the midpoint of bc, ar=rq=qc.prove that br=4sr

Answer 1

Answer:

Given A △ABC in which P is the mid-point of BC, Q is the mid-point of BC, Q is the mid-point of AP, such that BQ produced meets AC at R

To prove RA=

3

1

CA

Construction Draw PS||BR, meeting AC at S.

Proof In △BCR, P is the mid-point of BC and PS||BR.

∴ S is the mid−point of CR.

⇒ CS=SR

In △APS, Q is the mid-point of AP and QR||PS.

∴ R is the mid−point of AS

⇒ AR=RS

From (i) and (ii), we get

AR=RS=SC

⇒ AC=AR+RS+SC=3AR

⇒ AR=

3

1

AC=

3

1

CA [Hence proved]