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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)

Answers (1)


QP is the median of  \DeltaABQ
Therefore, ar(\DeltaPBQ) = 1/2. (ar \DeltaABQ)

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

Hence proved

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