ConceptPythagoras Theorem and Its Converse

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#### Question

P and Q are the mid-points of the sides CA and CB respectively of a ∆ABC, right angled at C. Prove that:

`(i) 4AQ^2 = 4AC^2 + BC^2`

`(ii) 4BP^2 = 4BC^2 + AC^2`

`(iii) (4AQ^2 + BP^2 ) = 5AB^2`

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