Question

Draw a circle with the help of a bangle. Take a point $P$ outside the circle. Construct the pair of tangents from this point $P$ to the circle.

Answer 1

Step 1: Draw a circle by tracing the surface of a bangle.

Step 2: Take a point $P$ outside the circle. Draw secant $P-R-Q$

Step 3: Place the compass on $P$ and mark two arcs on opposite side of $PQ$. Now, place the compass on $Q$ and draw two arcs intersecting the arcs drawn from $P$.

Step 4: Join the intersection points of the arcs to obtain the perpendicular bisector of $PQ$. Mark the mid point of $PQ$ as $M$.

Step 5: Place the compass on $M$ and taking $PM$ as radius draw a semicircle passing through $P$ and $Q$.

Step 6: From point $R$, draw a perpendicular to $PQ$ and let it intersect the semicircle drawn in step $5$ at $C$.

Step 7: Place the compass at $P$ and with $PC$ as radius, mark two arcs on the original circle and mark them as $A$ and $B$.

Step 8: Join $P-A$ and $P-B$

$PA$ and $PB$ are the required tangents.