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Question

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 $$ Q $$.


Solution

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.

1796013_1785674_ans_0ab6e400e71a4fd28e3df78f0cadb83a.png

Mathematics

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