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  • The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length <img alt="3 \mathrm{a}" src="https://entrancecorner.oncodecogs.c

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3 \mathrm{a} is

Option: 1

\mathrm{x}^{2}+\mathrm{y}^{2}=9 \mathrm{a}^{2}


Option: 2

\mathrm{x^{2}+y^{2}=16 a^{2}}


Option: 3

\mathrm{x^{2}+y^{2}=4 a^{2}}


Option: 4

\mathrm{x^{2}+y^{2}=a^{2}}


Answers (1)

best_answer

Since the triangle is equilateral, therefore centroid of the triangle is same as the circumcentre and radius of the circumcircle =2 / 3$ (median $)=2 / 3(3 a)=2 a.

Hence, the equation of the circumcircle whose centre is at (0,0) and radius 2 a is \mathrm{x^{2}+y^{2}=(2 a)^{2}}.

Posted by

Rishi

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