The equations of the sides AB , BC and CA of a triangle ABC are 2 x + 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 :

Question

The equations of the sides AB , BC and CA of a triangle ABC are 2 x + 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=9 p (B) ( AC )2+ p 2=136 (C) 32< operatornamearea( triangle ABC )<36 (D) 34< operatornamearea( triangle ABC )<38

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/9d3d77531ea1309b45fa60f49ad25d91-.png" /> Perpendicular bisector of A B x+y=5 Take image of A ( x -1/1)=( y +2/1)=(-2(-6)/2)=6 (7,4) 7+4 p =39 p =8 solving x +8 y =39 text and y =-2 x x =(-39/15) y =(78/15) AC 2=72=9 p AC 2+ p 2=72+64=136 Δ ABC =(1/2) | 1 -2 1 7 4 1 (-39/15) (78/15) 1| =(1/2)[4-(78/15)+2(7+(39/15))+7((78/15))+(4 × 39/15)] =(1/2)[18+18 × (13/5)] =9[(18/5)]=(162/5)=32.4

Q. The equations of the sides $A B, BC$ and $C A$ of a triangle $A BC$ are $2 x + y = 0, x + p y = 39$ and $x - y = 3$ respectively and $P (2, 3)$ is its circumcentre. Then which of the following is NOT true :

$(A C)^{2} = 9 p$

$(A C)^{2} + p^{2} = 136$

$32 < area (△ A BC) < 36$

$34 < area (△ A BC) < 38$

Q. 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 :

(AC)2=9p

(AC)2+p2=136

32<area(△ABC)<36

34<area(△ABC)<38

Q. The equations of the sides $A B, BC$ and $C A$ of a triangle $A BC$ are $2 x + y = 0, x + p y = 39$ and $x - y = 3$ respectively and $P (2, 3)$ is its circumcentre. Then which of the following is NOT true :

$(A C)^{2} = 9 p$

$(A C)^{2} + p^{2} = 136$

$32 < area (△ A BC) < 36$

$34 < area (△ A BC) < 38$