CBSE Class 9 Answered
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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 = 180o
Hence AGO =
BGO = 90o .
Similarly , we can prove CHO =
DHO = 90o .
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 180o , chords AB and CD are parallel.