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Math Help - Circle Question

  1. #1
    s3a
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    Circle Question

    I scanned the image with my visual work and I don't know where to go from there.

    Any help would be greatly appreciated!
    Thanks in advance!
    Attached Thumbnails Attached Thumbnails Circle Question-almostthere.jpg  
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  2. #2
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    The arc(PA)=50^o. The angle you want intercepts arc(PA)~\&~arc(BC).
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  3. #3
    s3a
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    How do you know that arc(DA) is 50?
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  4. #4
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    Quote Originally Posted by s3a View Post
    How do you know that arc(DA) is 50?
    What is the measure of arc(CBP)?
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  5. #5
    s3a
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    Again I think you confused the letter D for P. And I don't know how to find arc(CBD). Could you tell me please?
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  6. #6
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    Quote Originally Posted by s3a View Post
    Again I think you confused the letter D for P. And I don't know how to find arc(CBD).
    Well that could be. Your diagram is certainly shoddy.
    Surely you know that a diameter creates a half-circle?
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  7. #7
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    Hello, s3a!


    Draw AD.

    \Delta DAC is inscribed in a semicircle.

    . . Hence: . \angle DAC = 90^o \quad\Rightarrow\quad \angle DAB = 40^o \quad\Rightarrow\quad \text{arc}(DB) = 80^o \quad\Rightarrow\quad \angle DCB = 40^o


    In \Delta BEC\!:\;\;\angle BEC + \angle ECB + \angle CBE \:=\:180^o\quad\Rightarrow\quad \angle BEC \;+\; 40^o \;+\; 65^o \;=\;180^o

    Therefore: . \angle BEC \:=\:75^o

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