If A(b,c) B(-a,0) C(a,0) are the vertices of triangle ABC and P,Q are the mid points of overlineAB . overlineAC respectively and overlineBQ is perpendicular to overlineCP then

Question

If A(b,c) B(-a,0) C(a,0) are the vertices of triangle ABC and P,Q are the mid points of overlineAB . overlineAC respectively and overlineBQ is perpendicular to overlineCP then (A) b2 + c2 = 3a2 (B) b2 + c2 = 9a2 (C) c2 - b2 = 3a2 (D) a2 + b2 = 9c2

Tardigrade Admin · Accepted Answer

P((b-a/2), (c/2)) Q ((b+a/2) , (c/2)) Slope of BQ x Slope of CP = - 1

Q. If A(b,c) B(-a,0) C(a,0) are the vertices of triangle ABC and P,Q are the mid points of $\overline{A B} . \overline{A C}$ respectively and $\overline{BQ}$ is perpendicular to $\overline{CP}$ then

$b^{2} + c^{2} = 3 a^{2}$

$b^{2} + c^{2} = 9 a^{2}$

$c^{2} - b^{2} = 3 a^{2}$

$a^{2} + b^{2} = 9 c^{2}$

$P (\frac{b - a}{2}, \frac{c}{2})$
$Q (\frac{b + a}{2}, \frac{c}{2})$
Slope of BQ x Slope of CP = - 1

Q. If A(b,c) B(-a,0) C(a,0) are the vertices of triangle ABC and P,Q are the mid points of AB.AC respectively and BQ​ is perpendicular to CP then

b2+c2=3a2

b2+c2=9a2

c2−b2=3a2

a2+b2=9c2