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Chord Parallel to Diameter

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Intern
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Joined: 13 Aug 2008
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Chord Parallel to Diameter [#permalink]

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New post 21 Sep 2008, 02:29
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

This is a vague doubt, but can someone please shed some light on this:
You have a circle with center O and diameter AB and a chord CD parallel to AB. (Draw the figure such that points A and C lie on the same side of the circle). Join OC and BC.
Is it true that the line segment BC will bisect angle OCD i.e. angle OCB = angle BCD?

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Re: Chord Parallel to Diameter [#permalink]

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New post 22 Sep 2008, 01:55
Yes.

The reason is that in your figure, OC = OB and hence, angle OCB = angle OBC.

Now, since AB and CD are parallel lines, angle OBC = angle BCD.

Thus, angle, BCD = angle OCB and chord BC bisects angle OCD.

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Re: Chord Parallel to Diameter   [#permalink] 22 Sep 2008, 01:55
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