Chords in circle: If mAD = 58, m<AED = 42, find BC  TOPIC_SOLVED

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Chords in circle: If mAD = 58, m<AED = 42, find BC

Postby honest_denverco09 on Sat Apr 11, 2009 9:35 pm

In cirlce O, chords AB and CD intersect at E. If mAD = 58 and m<AED = 42, find BC
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Postby stapel_eliz on Sat Apr 11, 2009 10:33 pm

honest_denverco09 wrote:In cirlce O, chords AB and CD intersect at E. If mAD = 58 and m<AED = 42, find BC

Does "mAD" mean "the length of the arc from A to B"?

What have you tried so far? Please be complete, so we can "see" where you're having trouble.

Thank you! :D
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Re: Chords in circle: If mAD = 58, m<AED = 42, find BC

Postby Polyhymnio on Mon Jun 22, 2009 4:27 am

The measure of the angle between intersecting chords is equal to the mean of the measures of their intercepted arcs. Since <AED and <BEC are vertical angles, (mAD + mBC)/2 = 42. Then mBC = (42)(2) - 58 = 26

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Re: Chords in circle: If mAD = 58, m<AED = 42, find BC

Postby lizzy on Sat Jul 04, 2009 7:07 pm

I am really lost with this. i need major help!!!! :confused:It says that <AED and <BEC are verticle making <BEC measure also 42. So with that in mind how did they come to the conclusion that arc BC is twenty-six?
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Re: Chords in circle: If mAD = 58, m<AED = 42, find BC  TOPIC_SOLVED

Postby Polyhymnio on Sun Jul 05, 2009 6:20 am

42 is the mean (average) of the intercepted arcs. (mAD + mBC)/2 = 42. Since we know that mAD = 58, (58 + mBC)/2 = 42, (58 + mBC) = 84, mBC = 26

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