If A(((2c)/a) , (c/b)), B((c/a) , 0) and C(((1 + c)/a) , (1/b)) are three points, then prove that, i. (((AB)^2 + (BC)^2 )/((CA)^2 )) = ((c^2 + 1)/((c − 1)^2 )) ii. (AB)^2 + (BC)^2 − (AC)^2 = ((2c(a^2 + b^2 ))/(a^2 b^2 ))


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Question Number 191498 by MATHEMATICSAM last updated on 24/Apr/23

$If A (\frac{2 c}{a}, \frac{c}{b}), B (\frac{c}{a}, 0) and C (\frac{1 + c}{a}, \frac{1}{b})$ $are three points, then prove that,$ $i . \frac{{(AB)}^{2} + {(BC)}^{2}}{{(CA)}^{2}} = \frac{c^{2} + 1}{{(c - 1)}^{2}}$ $ii . {(AB)}^{2} + {(BC)}^{2} - {(AC)}^{2} = \frac{2 c (a^{2} + b^{2})}{a^{2} b^{2}}$
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