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 $\overline{AB} . \overline{AC}$ respectively and $\overline{BQ}$ is perpendicular to $\overline{CP}$ then

• A. $b^2 + c^2 = 3a^2$
• B. $b^2 + c^2 = 9a^2$
• C. $c^2 - b^2 = 3a^2$
• D. $a^2 + b^2 = 9c^2$

Answer 1

Answer: (B)

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