Question

in figure P is the midpoint of BC and Q is the midpoint of AP if BQ when produced meets AC at R prove that RA = 1 by 3 CA.​

Answer 1

In Δ BCR, P is the mid-point of BC and PL is parallel to BR.

Where, L is the mid-point of CR

So,   CL=LR----- (1)

Again, In Δ APL, Q is the mid-point of AP and QR  is parallel to PL.

Where, R is the mid-point of AL.

So,    AR=RL----- (2)

From equations (1) and (2),

We get, AL = RL = LC

⇒ AC=AR+RL+LC

⇒ AC=AR+AR+AR

⇒ AC=3AR

∴ RA=1/3AC

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Answer 2

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