Let the circle with centre at origin pass thr | vedclass

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(B) The circle is centered at the origin $(0, 0)$ and passes through $A(2, 4)$.The radius $R$ of the circle is the distance from the origin to $A$:$R

Vedclass · Accepted Answer

$3 \sqrt{5}$ units

Vedclass · Answer

(B) The circle is centered at the origin $(0, 0)$ and passes through $A(2, 4)$.The radius $R$ of the circle is the distance from the origin to $A$:$R = \sqrt{2^2 + 4^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5}$.In an equilateral triangle inscribed in a circle,the circumcenter is the same as the centroid.The distance from the centroid to a vertex is the circumradius $R$.The median from vertex $A$ passes through the centroid and has a total length $L = \frac{3}{2}R$.Substituting $R = 2\sqrt{5}$:$L = \frac{3}{2} 	imes 2\sqrt{5} = 3\sqrt{5}$ units.

Let the circle with centre at origin pass through the vertices of an equilateral triangle $ABC$. If $A = (2, 4)$,then the length of the median through $A$ is

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