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In figure, O is a point in the interior...

In figure, O is a point in the interior of a triangle ABC, `O D_|_B C ,O E_|_A C`and `O F_|_A B`. Show that
(i) `O A^2+O B^2+O C^2-O D^2-O E^2-O F^2=A F^2+B D^2+C E^2`
(ii) `A F^2+B D^2+C E^2=A E^2+C D^2+B F^2`

Text Solution

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In △ABC
`OD ⊥ BC`, `OE ⊥ AC`, and `OF ⊥ AB`
`OA`, `OB`, and `OC` joined as shown below. Using Pythagoras theorem, in `ΔOAF`,
...
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