Draw a circle with the help of a circular bangle. Construct two tangents to this circle from a point in the exterior of the circle.

(N/A) Data: Draw a circle with the help of a circular bangle and take point $A$ in the exterior of the circle.
To construct: Through $A$,tangents are to be drawn to the circle.
$(1)$ Draw a circle with the help of a circular bangle and take point $A$ in the exterior of the circle.
$(2)$ Draw two non-parallel chords $\overline{PQ}$ and $\overline{RS}$ in this circle.
$(3)$ Draw the perpendicular bisectors of $\overline{PQ}$ and $\overline{RS}$ to intersect each other at $O$. Here,$O$ is the centre of the circle drawn with the help of the circular bangle.
$(4)$ Draw $\overline{OA}$.
$(5)$ Obtain the midpoint $M$ of $\overline{OA}$ by constructing the perpendicular bisector of $\overline{OA}$.
$(6)$ Draw a circle with centre $M$ and radius $MA$ to intersect the first circle at $X$ and $Y$.
$(7)$ Draw rays $\overrightarrow{AX}$ and $\overrightarrow{AY}$.
Thus,$\overleftrightarrow{AX}$ and $\overleftrightarrow{AY}$ are the required tangents.