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.
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.