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

Geometric formulae, word problems, theorems and proofs, etc.
honest_denverco09
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### Chords in circle: If mAD = 58, m<AED = 42, find BC

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

stapel_eliz
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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!

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

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

Polyhymnio

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

I am really lost with this. i need major help!!!! 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?

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

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

Polyhymnio