the perpendicular from center of circle to a chord bisect the cords proff it
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GIVEN:-
A circle centre o and radius r
AB is chord of circle and OP perpendicular AB
To prove:-
AP=PB
Construction :-
Join OA and OB
Proff:-
In triangle OPA and OPB
Angle 1 = Angle 2 ( each 90 )
OA= OB ( radii of same circle )
OP = OP ( common )
By RHS Congrency
Triangle OPA is congrent to Triangle OPB
PA = PB ( C.P.C.T)
Therefore OP bisects AB
Note :-
Figure in attachment
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