CBSE Class 9 Answered

Question :-

If a diameter of circle bisect each of the chords of a circle prove that the chord are parallel.

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Figures shows the two chords AB and CD of circle are bisected by the diameter EF at G and H respectively.

Let o be the center of circle.

if we consider Δ OAG and Δ OBG , then we have

OA = OB  ( radii of circle )

GA = GB ( given )

side OG is common.

Hence ΔOAG and ΔOBG are congruent. 

AGO = BGO  and AGO + BGO = 180^o

Hence AGO = BGO = 90^o .

Similarly , we can prove CHO = DHO = 90^o .

if the diameter EF intrcepts the chords AB and CD , then AGO and CHO are interior angles .

Since sum of interior angles AGO and CHO is 180^o , chords AB and CD are parallel.