|hey mohit, its not AB=AC , but AB=BC and the thing is even if u make OB (which is radius) and from the fig. u can make out that since AC is perp. to CD therefore radius will be perp. to AC but still it is a kind of guess, as radius is perpendicular to every tangent but not to every chord unless specified|
see its nt a guess my friend, as u see abc will be an isosceles triangle so u know its median will also be a prependicular to a base and now frm circle's prespective we know that if we extend that isosceles trngle median bisector ,dats gonne be a radius why?? answer is prependicular drawn from the centre bisects the chord...a well known property ..hope this helps!!!!