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`A B C` is a right triangle right-angled at `C` . Let `B C=a ,\ \ C A=b ,\ \ A B=c` and let `p` be the length of perpendicular from `C` on `A B` , prove that (i) `c p=a b` (ii) `1/(p^2)=1/(a^2)+1/(b^2)`

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