Draw a circle of radius $$ 3 m $$ Take two prints $$ P $$ and $$ Q $$ on one its extended diameter each at a distance of $$ 7 cm $$ from its centre. Draw tangents to the circle from these two points $$ P $$ and $$ Q $$.
Steps of Construction : Step I : Taking a point $$ O $$ as center , draw a circle of radius $$ 3 cm $$ Step II : Take two points $$ P $$ and $$ Q $$ on one of its extended diameter such that $$ OP = OQ = 7 cm $$ Step III : Bisect $$ OP $$ and $$ OQ $$ and let $$ M_1 $$ and $$ M_2 $$ be the mid-points of $$ OP$$ and $$ OQ $$ respectively. Step IV : Draw a circle with $$ M_1 $$as center and $$ M_1 P $$ as radius to intersect the circle at $$ T_1 $$ and $$ T_2 $$ Strep V : Joint $$ PT_1 $$ and $$ PT_2 $$ Then $$ PT_1 $$ and $$ PT_3 $$ are the required tangents . Similarly the tangents $$ QT_3 $$ and $$ QT_4 $$ can be obtained. Justification ; On Joining $$ OT_1 $$ we find $$ \angle PT_O = 90^0 $$ as it is an angle in the semicircle. $$ \therefore PT_1 \bot OT_1 $$ Since $$ OT_1 $$ is a radius of the given circle , So $$ PT_1 $$ has to be the tangents to the circle. Similarly $$ PT_2, QT_3 $$ and $$ QT_4 $$ are also tangents to the circle.