If the incentre of an equilateral triangle is (1,1) and the equation of its one side is 3x…

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:

Accepted Answer

For an equilateral triangle, the incentre and circumcentre coincide, so the circumcentre is $(1,1)$.

Inradius $r=$ distance from $(1,1)$ to the given side $=\dfrac{|3+4+3|}{\sqrt{9+16}}=\dfrac{10}{5}=2$.

For an equilateral triangle $R=2r=4$.

Circumcircle: $(x-1)^2+(y-1)^2=16\Rightarrow x^2+y^2-2x-2y-14=0.$

Solutions · 1