Let A ( x 1, y 1), B ( x 2, y 2), C ( x 3, y 3) be three distinct points lying on circle S: x 2+ y 2=1 such that x1 x2+y1 y2+x2 x3+y2 y3+x3 x1+y3 y1=-(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 =(π/ 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 √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

Question

Let A ( x 1, y 1), B ( x 2, y 2), C ( x 3, y 3) be three distinct points lying on circle S: x 2+ y 2=1 such that x1 x2+y1 y2+x2 x3+y2 y3+x3 x1+y3 y1=-(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 =(π/ 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 √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 (A) P -3, Q-1, R-4, S-3 (B) P-4, Q-1, R-3, S-3 (C) P-3, Q-2, R-1, S-3 (D) P-2, Q-2, R-4, S-3

Tardigrade Admin · Accepted Answer

Correct answer is (a) P -3, Q-1, R-4, S-3

List- I		List- I I
P	Let $P$ be any arbitrary point lying on $S$ , then $(P A)^{2} + (PB)^{2} + (PC)^{2} =$	1	3
Q	Let the perpendicular dropped from point ' $A$ ' to $BC$ meets $S$ at $Q$ and $∠ OBQ = \frac{π}{k}$ , 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 $a + b b$ , then $a + b =$ (Given $a$ and $b$ are distinct natural numbers)	3	6
S	Let $I$ and $G$ represent incentre and centroid of $△ A BC$ respectively, then $I A + I B + I C + G A + GB + GC =$	4	5