Steps of Construction:

Step I: With O as a centre and radius equal to 3 cm, a circle is drawn.

Step II: The diameter of the circle is extended both sides and an arc is made to cut it at 7 cm.

Step III: Perpendicular bisector of OP and OQ is drawn and x and y be its mid-point.

Step IV: With O as a centre and Ox be its radius, a circle is drawn which intersected the previous circle at M and N.

Step V: Step IV is repeated with O as centre and Oy as radius and it intersected the circle at R and T.

Step VI: PM and PN are joined also QR and QT are joined.

Thus, PM and PN are tangents to the circle from P and QR and QT are tangents to the circle from point Q.

Justification:

∠PMO = 90° (Angle in the semi circle)

∴ OM ⊥ PM

Therefor, OM is the radius of the circle then PM has to be a tangent of the circle.

Similarly, PN, QR and QT are tangents of the circle.