Question

The four distinct points $(0,0),(2,0),(0,-2)$ and $(k,-2)$ are con-cyclic if $k=$

• A. $2$
• B. $-2$
• C. $0$
• D. $1$

Answer 1

The correct option is A $2$

Angle formed by semicircle is right angle.

Then, point $A(2,0)$ and $C(0,-2)$ are diameter extremities

Centre of the circle $=(+1,-1)$

Equation of circle is

$(x-1{)}^2+(y+1{)}^2=(\frac{AC}{2}{)}^2$

$(x-1{)}^2+(y+1{)}^2=2$

So, $(k,-2)$ satisfy to this equation,

$(k-1{)}^2+(1{)}^2=2$

$(k-1{)}^2=1$

So, $k=2$