Answer:
Given, Two tangents AM and AN are drawn from point A to a circle with centre O. To Prove: \[AM=AN\] Construction: Join \[OM,ON\] and \[OA\]. Proof: Since, \[AM\] is a tangent and \[OM\] is a radius. \[\therefore OM\bot AM\] Similarly, \[ON\bot AN\] Now, in \[\Delta \,OMA\] and \[\Delta \,ONA\] \[OA=OA\] (Common) \[OM=ON\] (Radii of the circle) \[\angle OMA=\angle ONA=90{}^\circ \] \[\therefore \Delta \,OMA\cong \Delta \,ONA\] (By RHS congruence) Hence, \[AM=AN\] Hence Proved.
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