Question

If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is $3x + 4y + 3 = 0$, then the equation of the circumcircle of this triangle is :

• A. $x^{2}+y^{2}-2x-2y-2=0$
• B. $x^{2}+y^{2}-2x-2y-14=0$
• C. $x^{2}+y^{2}-2x-2y+2=0$
• D. $x^{2}+y^{2}-2x-2y-7=0$

Answer 1

Answer: (B)

Let radius of circumcircle be According to the question,
$\frac{r}{2}=\frac{10}{5} \Rightarrow r=4$
So equation of required circle is
$\left(x-1\right)^{2}+\left(y-1\right)^{2}=16$
$\Rightarrow x^{2}+y^{2}-2x-2y-14=0$