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Consider the triangle ABC with vertices ...

Consider the triangle ABC with vertices ` A (-2,3), B (2, 1)` and `C(1,2)`. What is the circumcentre of the triangle ABC?

A

(-2, -2)

B

(2, 2)

C

(-2, 2)

D

(2, -2)

Text Solution

Verified by Experts

The correct Answer is:
A
A circumcentre is a point at which perpendicular bisectors meet each other.
Here, 'E' represents circumcentre

Mid-point of `BC=((2+1)/2, (1+2)/2)=(3/2, 3/2)`
Slope of `BC=(2-1)/(1-2)=-1`
`:.` Slope of `DE=1`
Now, equation of `vec(ED)` is `(y-3/2)=1 (x-3/2)`
`:. 2y-3=2x-3`
`:. x=y` ...(i)
Now, mid-point of `AC=((-2+1)/2, (3+2)/2)=(-1/2, 5/2)`
Slope of `AC=(3-2)/(-2-1)=-1/3`
`:.` Slope of `EF=3`
Now, equation of `vec(EF)` is `(y-5/2)=3 (x+1/2)`
`:. 2y-5=6x+3` ...(ii)
From equations(i) and (ii),
`x=-2 and y=-2`
Hence, circumcentre of `Delta ABC` is `(x, y)=(-2, -2)`
`:.` Option (a) is correct.
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