Question

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

• A. $(AC)^2 = 9p$
• B. $(AC)^2 + p^2 = 136$
• C. $32 < area (ΔABC)<36$
• D. $34<area(ΔABC)<38$

Answer 1

Answer: (D)

$34<area(ΔABC)<38$

Answer 2

The correct answer is (D) : $34<area(ΔABC)<38$
Intersection of 2x + y = 0 and x – y = 3 :A(1, –2)

Fig.

Equation of perpendicular bisector of AB is
x – 2 y = –4
Equation of perpendicular bisector of AC is
_x _+ y = 5
Point B is the image of A in line x – 2 y + 4 = 0
which can be obtained as
$B(\frac{-13}{5},\frac{26}{5})$
Similarly vertex C : (7, 4)
Equation of line BC : x + 8 y = 39
So, p = 8
$AC = \sqrt{(7-1)^2+(4+2)^2}$
$= 6\sqrt2$
Area of triangle ABC = 32.4