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Math Help - Circle Geometry:Finding Unknown Angle

  1. #1
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    Circle Geometry:Finding Unknown Angle

    In diagram arc BC is three times larger than arc AD and angle BEC = 80. Let angle ABD = x and find x.

    Here i cannot include the given information into the question. So using the 80 alone, i cannot get any angles...
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Lukybear View Post
    In diagram arc BC is three times larger than arc AD

    Here i cannot include the given information into the question. So using the 80 alone, i cannot get any angles...

    Let O be the centre of circle.
    since arcBC is three times arcAD, hence
    angle BOC is three times angle AOD(why?)

    Can you proceed from here?
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    We know that 2m\left( {\angle BEC} \right) = m\left( {arc(DA)} \right) + m\left( {arc(BC)} \right).
    So what is m\left( {arc(DA)} \right)?
    We know that 2m\left( {\angle ABD} \right) = m\left( {arc(DA)} \right).
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    I have no idea malaygoel how to proceed from there. That was the original information i know. Could you please expand on that? For i think thats the method the question wants the students to develop.

    Also plato, really sorry, but i cant understanding your use of symbols. Wha is m?
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  5. #5
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    Quote Originally Posted by Lukybear View Post
    Also plato, really sorry, but i cant understanding your use of symbols. Wha is m?
    With all due respect, it you have no idea about what I wrote in my reply then you are simply not at the level of mathematical maturity to have been assigned this question.
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    Well mabey. But i do think since i am in a different part of the world, that different symbology apply to same meaning.

    But without going into that, i am still very interested in what m means. I understanding arc and angle. Considering what you are saying, you might be right. Then i would assume that a easier, more fundemental approach to this question was suitable.
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  7. #7
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    circle

    Let O be the center of the circle

    It is given that

    \angle{BOC} = 3\angle{AOD}

    Now \angle{BOC} = 2 \angle{BAC}

    and \angle{AOD} = 2\angle{ABD}

    But \angle{BAC} + \angle{ABD}= 80 degrees

    Substitute the values and find angle ABD.
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  8. #8
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    just a comment

    The measure (m) 0f an angle between two chords in a circle equals half the sum of its arcs.


    bjh
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  9. #9
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    m[angle ABC] means "measure" of angle ABC: always thought that was silly and misleading.

    Like for line AB = x, we don't use m[line AB] = x; so why treat angles differently?

    That's my opinion: I respect yours, but if it's not same as mine, then it's wrong
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  10. #10
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    Quote Originally Posted by sa-ri-ga-ma View Post
    Let O be the center of the circle

    It is given that

    \angle{BOC} = 3\angle{AOD}

    Thxs very much. Its so easy once ive seen it.

    Now \angle{BOC} = 2 \angle{BAC}

    and \angle{AOD} = 2\angle{ABD}

    But \angle{BAC} + \angle{ABD}= 80 degrees

    Substitute the values and find angle ABD.
    Thxs so much. Once ive seen it it becomes so easy.
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