• # question_answer 18) Prove that the lengths of tangents drawn from an external point to a circle are equal.

 Given: a circle with centre O on which two tangents PM and PN are drawn from an external point P. To prove: PM = PN Construction: Join OM, ON and OP. Proof: Since tangent and radius are perpendicular at point of contact, $\therefore$    $\angle OMP=\angle ONP=90{}^\circ$ In $\Delta \text{ }POM$and $\Delta \text{ }PON$, $OM=ON$                                      (Radii) $\angle OMP=\angle ONP$ $PO=OP$                    (Common) $\therefore$      $\Delta \,OMP\cong \Delta \,ONP$                            (RHS cong.) $\therefore$        $PM=PN$                              (CPCT) Hence Proved.