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
(ii)
In RBC, RQ is the median
Therefore ar(RQC) = ar(RBQ)
= ar (PRQ) + ar (BPQ)
= 1/8 (ar ABC) + ar(BPQ) [from eq (vi) & eq (A) in part (i)]
= 1/8 (ar ABC) + 1/2 (ar PBC) [ since PQ is the median of BPC]
= 1/8 (ar ABC) + (1/2).(1/2)(ar ABC) [CP is the medain of ABC]
= 3/8 (ar ABC)
Hence proved.