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# P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that (iii) ar (PBQ) = ar (ARC)

Q : 7     P and  Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that

(iii) $ar (PBQ) = ar (ARC)$

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QP is the median of  $\Delta$ABQ
Therefore, ar($\Delta$PBQ) = 1/2. (ar $\Delta$ABQ)

= (1/2). (1/2) (ar $\Delta$ABC) [since AQ is the median of $\Delta$ABC
= 1/4 (ar $\Delta$ABC)
= ar ($\Delta$ ARC)    [from eq (A) of part (i)]

Hence proved

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