If $p_1,p_2,p_3$ are respectively the perpendiculars from the vertices of a triangle to the opposite sides, then $p_1{p}_2{p}_3=$

Q. If $p_1,p_2,p_3$ are respectively the lengths of perpendiculars from the vertices of a triangle $ABC$ to the opposite sides then
(i) $\frac{\cos A}{p_1}+\frac{\cos B}{p_2}+\frac{\cos C}{p_3}=\frac{1}{R}$
(ii) $\frac{b{p}_1}{c}+\frac{c{p}_2}{a}+\frac{a{p}_3}{b}=\frac{a^2+b^2+c^2}{2R}$.

Q. Assertion :In any right angled triangle $\frac{a^2+b^2+c^2}{R^2}$ is always equal to $8$. Reason: $a^2=b^2+c^2$ or $b^2=c^2+a^2$ or $c^2=a^2+b^2$

Q. Consider the planes
$P_1:cy+bz=x$
$P_2:az+cx=y$
$P_3:bx+ay=z.$
$P_1,P_2$ and $P_3$ pass through one line, if

Q. If $P_1,P_2,P_3$ are lengths of perpendicular from vertices A, B, C respectively of a $△ABC$, then prove that
$R=\frac{1}{4}\frac{a^2+b^2+c^2}{P_{1}cosA+P_{2}cosB+P_{3}cosC}$

Q. Assertion :In any right angled triangle $\frac{a^2+b^2+c^2}{R^2}$ is always equal to $8$ Reason: $a^2=b^2+c^2$