Question

Assertion :If the centroid of an equilateral triangle is $(2,2)$ and its one vertex is $(-3,4)$, then the equation of its circumcircle is $x^2+y^2-4x-4y-21=0$ Reason: Circumcircle coincides with the centroid of an equilateral triangle.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Since the circumcentre coincides with the centroid of an equilatersal triangle,

$\therefore$ Circumcenter is $(2,2).$

Radius $=\sqrt{{(2+3)}^2+{(2-4)}^2}=\sqrt{29}$

$\therefore$ The equation of the circumcircle is

${(x-2)}^2+{(y-2)}^2=29\Rightarrow x^2+y^2-4x-4y-21=0.$