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# Draw a circle of radius 3 cm. Take two points P and Q on one of 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 to construct the required figure:
Step 1:Draw a circle of radius 3cm and mark it’s center as O.

Step 2:Extend the diameter in both the direction as shown in the figure and mark the points as P and Q such that OP=OQ=7 cm.

Step 3: Mark the midpoint of OP and OQ as M and M’ respectively.

Step 4:With these points as M and M’, draw circles of radius MP and MO respectively.

Step 5: Circles with the center M intersects the first circle at R and S and the circle with center M’ intersects the first circle at T and U.

Step 6: Join PR,PS,QT and QU

Thus we have got the pair of tangents as PR and PS from point P and OT and QU as another pair of tangent from point Q drawn to the circle.

JUSTIFICATION:

Join OR and we have in triangle PRO,

∠PRO=90° [ Angle in a semicircle]

Also OR is the radius of the circle with center O.

$$\therefore$$ Line PR$$\perp$$ OR

We know that a line drawn through the end of a radius and perpendicular to it is a tangent to the circle. Hence, we have PR as the tangent to the point R and similarly ,PS,QT and QU as the tangents at the points S,T and U respectively.