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Question

The equations of the sides $\mathrm{AB}, \mathrm{BC}$ and CA of a triangle ABC are $2 x+y=0, x+\mathrm{p} y=39$ and $x-y=3$ respectively and $\mathrm{P}(2,3)$ is its circumcentre. Then which of the following is NOT true?

$(\mathrm{AC})^{2}=9 \mathrm{p}$
$(\mathrm{AC})^{2}+\mathrm{p}^{2}=136$
$32<\operatorname{area}\,(\Delta \mathrm{ABC})<36$
$34<\operatorname{area}\,(\triangle \mathrm{ABC})<38$

Solution

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