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P and Q are the mid-points of the CA ...

P and Q are the mid-points of the CA and CD respectively of a triangle ABC,  right angled at C. Prove that: `4AQ^2 = 4AC^2 + BC^2`, `4BP^2 = 4BC^2 + AC^2`, and `4(AQ^2 + BP^2) = 5AB^2`.

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