The chord of contact of tangents from 3 points $A, B, C$ to the circle $x^2+y^2=a^2$ are concurrent, then $A, B, C$ will

 

Let the coordinates of$A, B$and $C$ be $\left(x_1,y_1\right), \left(x_2, y_2\right)$

and $\left(x_3, y_3\right)$ respectively. Then, the chords of contact of tangents drawn from $A , B$ and$C$ are

$x{x}_1+y{y}_1=a^2,x{x}_2+y{y}_2=a^2$ and $x{x}_3+y{y}_3=a^2$

respectively. These three lines will be concurrent, if

$\left|\begin{array}{ccc}{x}_1& y_1& -a^2\\ x_2& y_2& -a^2\\ x_3& y_3& -a^2\end{array}\right|=0$

$\Rightarrow -a^2\left|\begin{array}{l}{x}_1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{y}_1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\\ x_2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{y}_2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\\ x_3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{u}_3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\end{array}\right|=0\Rightarrow \left|\begin{array}{l}{x}_1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{y}_1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\\ x_2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{y}_2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\\ x_3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{y}_3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\end{array}\right|=0$

which is the condition of collinearity of points $A, B, C$.