Sarthaks Test
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In a ∆ABC, P and Q are respectively the mid-points of AB and BC and R is the mid-point of AP. Prove that : 

(i) ar (∆ PBQ) = ar (∆ ARC) 

(ii) ar (∆ PRQ) = 1/2 ar (∆ ARC) 

(iii) ar (∆ RQC) = 3/8 ar (∆ ABC). 

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(i) We know that each median of a ∆le divides it into two triangles of equal area 

Since, OR is a median of ∆CAP

(ii) Since QP and QR medians of ∆s QAB and QAP respectively.

(iii) Since, ∠R is a median of ΔCAP

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