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Math Help - Circle O

  1. #1
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    Circle O

    In Circle O, chord AB is parallel to chord CD. AD and BC go through the center of this circle. If the measure of angle BOA is 40 degrees and the measure of arc CD is 70 degrees, find the measure of arc BD.

    I found the answer to be 110 degrees but the correct answer is 95 degrees. How do I get 95 degrees here?
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    In Circle O, chord AB is parallel to chord CD. AD and BC go through the center of this circle. If the measure of angle BOA is 40 degrees and the measure of arc CD is 70 degrees, find the measure of arc BD.

    I found the answer to be 110 degrees but the correct answer is 95 degrees. How do I get 95 degrees here?
    Hi magentarita,

    Something is messed up in these circle questions you're presenting. You are descibing two intersecting diameters, AD and BC, that form vertical angles at the center of circle O.

    If angle BOA = 40 degrees, then angle DOC = 40 degrees because vertical angles have equal measures.

    That would make arc CD = 40 degrees since the measure of a central angle is the same as its subtended arc. But you said arc CD = 70 degrees, and that's not possible.
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  3. #3
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    ok....

    Quote Originally Posted by masters View Post
    Hi magentarita,

    Something is messed up in these circle questions you're presenting. You are descibing two intersecting diameters, AD and BC, that form vertical angles at the center of circle O.

    If angle BOA = 40 degrees, then angle DOC = 40 degrees because vertical angles have equal measures.

    That would make arc CD = 40 degrees since the measure of a central angle is the same as its subtended arc. But you said arc CD = 70 degrees, and that's not possible.
    No wonder I was not able to find the answer. The book has many errors and this is one of them. This is why I decided to place the questions here as with all the questions that I have placed in this forum since day one. When something does not make sense, I come to this forum for help.
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