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