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JEE Main202324 Jan 2023Evening ShiftMathematicsStraight LinesActual

The equations of the sides A B , B C & C A of a triangle A B C are 2 x + y = 0 , x + p y = 21 a a ≠ 0 and x - y = 3 respectively. Let P 2 , a be the centroid of the triangle A B C , then B C 2 is equal to

Correct answer

0

Step-by-step solution

We have, Since, G 2 , a , so 1 + α + β + 3 3 = 2 and - 2 - 2 α + β 3 = a ⇒ α + β = 2 and - 2 α + β = 3 a + 2 So, α = - a ,   β = 2 + a So, B ≡ - a , 2 a ,   C ≡ 5 + a , 2 + a Now, B and C lies on the line x + p y = 21 a , so - a + 2 p a = 21 a ⇒ p = 11 Also, 5 + a + 11 2 + a = 21 a ⇒ 27 = 9 a ⇒ a = 3 So, B ≡ - 3 , 6 ,   C ≡ 8 , 5 So, B C 2 = 121 + 1 = 122

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