Question:
An equilateral triangle is inscribed in the circle x²+y²=a² with one of the vertices at (a,0). What is the equation of the side opposite to this vertex?
An equilateral triangle is inscribed in the circle x²+y²=a² with one of the vertices at (a,0). What is the equation of the side opposite to this vertex?
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Equilateral triangle in a circle uses 120^∘ angular separation.
Updated On: Mar 19, 2026
- 2x+a=0
- x+a=0
- 2x-a=0
- 3x-2a=0
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The Correct Option is A
Solution and Explanation
Vertices of the equilateral triangle on the circle are at angles 0^∘,120^∘,240^∘.
Coordinates of the other two vertices:
(-(a)/(2),±frac√(3)a2)
Both have the same x-coordinate, so the opposite side is:
x=-(a)/(2)⟹ 2x+a=0
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