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  • The equations of the sides AB, BC and CA of a triangle ABC are : <img alt="2 x+y=0, x+p y=21 a,(a \neq 0)" src="https://entrancecorner.oncodecogs.com/gif.latex?2%20x&plus;y%3D0%2C%20x&

The equations of the sides AB, BC and CA of a triangle ABC are : 2 x+y=0, x+p y=21 a,(a \neq 0) and x - y = 3 respectively. Let P(2,a) be the centroid of \Delta ABC Then (BC)^{^{2}} is equal to 

Option: 1

122


Option: 2

"__"


Option: 3

"__"


Option: 4

"__"


Answers (1)

\begin{array}{ll} \frac{\alpha+\beta+4}{3}=2 & \frac{-2 \alpha-2+\beta}{3}=a \\ \alpha+\beta=2 & -2 \alpha+\beta=3 \mathrm{a}+2 \\ & -2 \alpha+2-\alpha=3 \mathrm{a}+2 \\ & \alpha=-\mathrm{a} \end{array}

put 'B' in BC

\begin{array}{ll} \alpha-2 p \alpha=21 a & \\ \alpha .(1-2 p)=21 \mathrm{a} \quad & 2 p-1=21 \\ & p=11 \end{array}

put 'C' in BC

\begin{aligned} &\begin{aligned} & \beta+3+11 \beta=21 a \\ & 21 \alpha+12 \beta+3=0 \\ & \text { also } \beta=2-\alpha \end{aligned}\\ &\begin{gathered} \text { Solving } \alpha=-3, \beta=5 \\ \therefore \mathrm{BC}=\sqrt{122} \\ \mathrm{BC}^2=122 \end{gathered} \end{aligned}

 

Posted by

Ramraj Saini

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