(N/A) To construct tangents to a circle drawn with a bangle (where the centre is unknown):
$1$. Draw two non-parallel chords $BC$ and $CD$.
$2$. Draw the perpendicular bisectors of $BC$ and $CD$. The point where these bisectors intersect is the centre $E$ of the circle.
$3$. Take a point $A$ outside the circle. Join $AE$.
$4$. Bisect $AE$ at point $F$. With $F$ as the centre and $FA$ as the radius,draw a circle.
$5$. Let this circle intersect the original circle at points $B$ and $G$. Join $AB$ and $AG$.
$AB$ and $AG$ are the required tangents.
Justification:
Join $EB$ and $EG$. $\angle ABE$ is an angle in a semi-circle,so $\angle ABE = 90^{\circ}$. Since $EB$ is a radius,$AB$ must be a tangent. Similarly,$\angle AGE = 90^{\circ}$,so $AG$ is a tangent.