P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and Ris the mid-point of AP, show that (i) `a r (P R Q)=1/2a r(A R C)`(ii) `a r (R Q C)=3/8a r (A B C)`(iii) `a r (P B Q) =a r (ARC)`

Explanation

(i)From APQ we have,
`ar.(APQ)`

`=½*(1/2)ar.(ABQ) `

`=(1/2)*(1/2)*(1/2)ar.(ABC) `

`=(1/8)ar.(ABC) ————–(1)`

Similarly from,v
`ar.(ARC)=(1/2)(APC) `v
`=(1/2)*(1/2)ar.(ABC) `

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