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In a right triangle ABC right angled at C, P and Q are points on sides AC and CB respectively which divide these sides in the ratio of 2 : 1.
Prove that (i) `9 AQ^(2) = 9AC^(2) + 4BC^(2)`
(ii) `9BP^(2) = 9BC^(2) + 4AC^(2)`
(iii) 9`(AQ^(2) + BP^(2)) = 13 AB^(2)`

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