Question

Draw a circle of radius $3cm$. Take two points $P$ and $Q$ on one of its extended on both sides of its centre, each at a distance of $7cm$ on opposites of its centre. Draw tangents to the circle from each of these two points $P$ and $Q$

Answer 1

Step 1: Draw a circle with centre $O$ and radius $3cm$ using a compass.

Step 2: Draw a secant passing through the centre. Mark points $P$ and $Q$ on opposite sides of the centre at a distance of $7cm$ from $O$.

Step 3: Place the compass on $P$ and draw two arcs on opposite sides of $OP$. Now place the compass on $O$ and draw two arcs intersecting the arcs drawn from point $P$.

Step 4: Join the intersection points of the arcs to obtain the perpendicular bisector of $OP$. Mark the mid point of $OP$ as $M_1$

Step 5: From $M_1$ draw a circle with radius $=M_{1}P=M_{1}O$

Step 6: Mark the intersection points of the circle drawn from $M_1$ with the circle drawn from $O$ as $A$ and $B$.

Step 7: Join $P-A$ and $P-B$

Step 8: Repeat steps $3$ to $7$ for point $Q$ and obtain tangents $QC$ and $QD$

$PA,PB,QC$ and $QD$ are the required tangents.