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?
Solutions · 1
Official solution
Intersection of 2x+y=0 and \[x - y = 3\,:\,A(1, - 2)\]
Equation of perpendicular bisector of AB is
x−2y=−4
Equation of perpendicular bisector of AC is
x+y=5
Point B is the image of A in line x−2y+4=0 which is obtained as \[B\left( {{{ - 13} \over 5},{{26} \over 5}} \right)\]
Similarly vertex C:(7,4)
Equation of line BC:x+8y=39
So, p=8
\[AC = \sqrt {{{(7 - 1)}^2} + {{(4 + 2)}^2}} = 6\sqrt 2 \]
Area of triangle ABC=32.4