The equation of a circle with origin as a centre and passing through equilateral triangle whose medi

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The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is

Accepted Answer

Let ABC be an equilateral triangle, whose median is AD.
Given AD = 3a
In ᐃABD, AB² = AD² + BD² ;
⇒ x² = 9a² + (x²/4) whereAB = BC = AC = x. x² = 9a² ⇒ x² = 12a²
In ᐃOBD, OB² = OD² + BD²
⇒ r² = (3a - r)² + ⇒ r² = 9a² - 6ar + r² + 3a² ; ⇒ 6ar = 12a² ⇒ r = 2a
So equation of circle is x² + y² = 4a²

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