In a right triangle ABC, right angled at C, P and Q are points of the sides CA and CB respectively,which divide these sides in the ratio 2: 1. Prove that(I) 9AQ2= 9AC2+4BC2 (II) 9 BP2= 9 BC2 + 4AC2(III) 9 (AQ2+BP2) = 13AB

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