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Math Help - ~~**circle geometry**~~

  1. #1
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    ~~**circle geometry**~~

    in a triangle ABC, AC=BC and angle ACB=40. The vertices A,B and C lie on the circumference of a cirlce. D is a point outside this circle such that DC is perpendicular to BC, BC=DC and the points B and D are on the same side of the line AC. DA cuts the circumference of the circle at E. Find the size of angle BCE.




    any help would be great
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  2. #2
    Member Glaysher's Avatar
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    This situation?
    Attached Thumbnails Attached Thumbnails ~~**circle geometry**~~-circle.png  
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  3. #3
    Member Glaysher's Avatar
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    ABC isosceles

    So angle ABC = \frac{180-40}{2}=70

    Also angle BAC and angle AEC = 70 (by isosceles and circle theorem)

    ACD isosceles

    So angle CAE = \frac{180-40-90}{2}=25

    Call unmarked point P where lines cross

    angle APC = 180 - 25 - 40 = 115

    So angle CPE = 65

    So angle BCE = 180 - 65 - 70 = 45
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  4. #4
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    Quote Originally Posted by Glaysher

    Also angle BAC and angle AEC = 70 (by isosceles and circle theorem)
    what is the circle theorum?
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  5. #5
    Member Glaysher's Avatar
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    There are lots of circle theorems. This is a link for them. I used the first one.

    http://www.mathsrevision.net/gcse/pages.php?page=13
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  6. #6
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    Quote Originally Posted by Glaysher
    There are lots of circle theorems. This is a link for them. I used the first one.

    http://www.mathsrevision.net/gcse/pages.php?page=13
    Thanks
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