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An equilateral triangle is inscribed in ...

An equilateral triangle is inscribed in the circle `x^2+y^2=a^2` with one of the vertices at (a,0). What is the equation of the side opposite to this vertex ?

A

`2x-a = 0`

B

`x+a= 0`

C

`2x+a = 0`

D

`3x-2a=0`

Text Solution

Verified by Experts

The correct Answer is:
C
Since the equilateral is inscribed in the circle with centre at the origin, centroid lies on the origin.
So, `(AO)/(OD) = 2/1`
and `OD = 1/2AO = a/2`
So, other vertices of a triangle have coordinates,
`(-a/2, (sqrt(3a))/(2))` and `[-a/2, - (sqrt(3))/(2)a]`
`(-a/2(sqrt(3))/(2)a)`

`(-a/2, (-sqrt(3a))/(2))`
`:.` Equation of line `BC` is :
`x = -a/2`
`rArr 2x +a = 0`
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