Question

In the figure, $C$ is the centre of the circle. $X$ and $Y$ axes are tangents to the circle at the points $A$ and $B$ respectively. If the coordinates of $A$ are $(4,0)$, find the coordinates of $B$ and $C$.

Answer 1

Since tangents drawn from an external point to a circle are equidistant, we have $OA=OB=4$
Thus, co-ordinates of $B$ are $(0,4)$.
Construction: Draw perpendicular from centre $C$ to the x-axis at point $A$ and y-axis at point $B$.
Now, it is clear from the figure that $OA=BC=4$, the x-coordinate of the centre $C$ is $4$.
Similarly, since $OB=AC=4$, the y-coordinate of the centre $C$ is $4$.
Thus, co-ordinates of $C$ are $(4,4)$.