Q.
Let $A \left( x _1, y _1\right), B \left( x _2, y _2\right), C \left( x _3, y _3\right)$ be three distinct points lying on circle $S : x ^2+ y ^2=1$ such that $x_1 x_2+y_1 y_2+x_2 x_3+y_2 y_3+x_3 x_1+y_3 y_1=-\frac{3}{2}$
Match the following:
List- I
List- I I
P
Let $P$ be any arbitrary point lying on $S$, then $( PA )^2+( PB )^2+( PC )^2=$
1
3
Q
Let the perpendicular dropped from point ' $A$ ' to $BC$ meets $S$ at $Q$ and $\angle OBQ =\frac{\pi}{ k }$, where ' $O$ ' is origin, then $k =$
2
4
R
Let $R$ be the point lying on line $x + y =2$, at the minimum distance from $S$ and the square of maximum distance of $R$ from $S$ is $a+b \sqrt{b}$, then $a+b=$ (Given $a$ and $b$ are distinct natural numbers)
3
6
S
Let $I$ and $G$ represent incentre and centroid of $\triangle ABC$ respectively, then $IA + IB + IC + GA + GB + GC =$
4
5
| List- I | List- I I | ||
|---|---|---|---|
| P | Let $P$ be any arbitrary point lying on $S$, then $( PA )^2+( PB )^2+( PC )^2=$ | 1 | 3 |
| Q | Let the perpendicular dropped from point ' $A$ ' to $BC$ meets $S$ at $Q$ and $\angle OBQ =\frac{\pi}{ k }$, where ' $O$ ' is origin, then $k =$ | 2 | 4 |
| R | Let $R$ be the point lying on line $x + y =2$, at the minimum distance from $S$ and the square of maximum distance of $R$ from $S$ is $a+b \sqrt{b}$, then $a+b=$ (Given $a$ and $b$ are distinct natural numbers) | 3 | 6 |
| S | Let $I$ and $G$ represent incentre and centroid of $\triangle ABC$ respectively, then $IA + IB + IC + GA + GB + GC =$ | 4 | 5 |
JEE AdvancedJEE Advanced 2022
Solution: