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Geometry - Chord of a circle

  1. Nov 3, 2014 #1
    1. The problem statement, all variables and given/known data
    Attached here is a diagram. My questions are, how to compute for the value of the chord? How to compute for the value of the tangential line? Please help.. Thank you in advance.
     

    Attached Files:

  2. jcsd
  3. Nov 3, 2014 #2

    BvU

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    Oops, the template got lost. Programming error or accidental deletion? Here it is again: :)
    1. The problem statement, all variables and given/known data
    2. Relevant equations
    3. The attempt at a solution


    Also, you want to ask clear questions. "Value of a chord" is not very scientific: Economic value ? Color value ? In this case you want the length.
    Seems to me that one needs the circle radius also to make sense of this ?
     
  4. Nov 3, 2014 #3
    Sorry about the template.


    1. The problem statement, all variables and given/known data

    Problem statement:

    Find the value of the chord (blue line) and at the same time the value of the tangential line.

    Given data:
    Red line = 6
    Green Line = 3
    Radius of the Circle = 2

    2. Relevant equations
    I dont know any equations that can solve the problem :(

    3. The attempt at a solution
    I used the area of a trapezoid. But too many unknown.
     
  5. Nov 3, 2014 #4

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    Tangent.jpg
    This help ? I see a way to calculate distance top left to center cicle, and then top left to tangent point.
    And then there are isomorphic triangles to be found that can help us further...
     
  6. Nov 3, 2014 #5
    From there, can I use pythagorean theorem to solve the value of the tangential line? :)
     
  7. Nov 3, 2014 #6

    BvU

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    value being length, equation, whatever: yes, I should think so. Didn't work it all out in detail: your job. Finding a possible smarter way is also your job/challenge :)
     
  8. Nov 3, 2014 #7
    Can you give me hints on how can I relate the length of the tangent line to the chord? Pleaseee. Thank you :)
     
  9. Nov 3, 2014 #8

    BvU

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    Tangent2.jpg
    Draw AD, calculate |AD|, calculate |AB| .
    Look at isomorphic triangles ACE and DCE
    then DCE and BCF
    Looks like a lot of work. You do some too.
     
  10. Nov 3, 2014 #9
    Hmm.. Since, the tangent line and Radius is perpendicular, then it creates a 90degrees. The other side is also 90degrees, would it be right if I use 45degrees for the chord line and the radius? :)
     
  11. Nov 4, 2014 #10

    BvU

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    More questions, no work done yet. What about AD and AB?
     
  12. Nov 6, 2014 #11
    Hmmm ....
    It seems that DCE isn't a triangle at all, since the 3 points are collinear!
     
  13. Nov 6, 2014 #12
    There are several assumptions made here:
    1) The black lines are all tangent to the circle
    2) The vertical tangent line, the red line, and the blue line are all parallel to each other
    3) The green lines are perpendicular to the vertical tangent line
    4) The red line bisects both green lines
    5) The midpoint of the red line is collinear with the center of the circle and the tangent point of the vertical tangent line.

    By "value of the tangent line," I assume he means the length of a segment of the vertical tangent line between the points where it intersects the other 2 tangent lines?
    Also, the OP doesn't specify which tangent line
     
  14. Nov 6, 2014 #13

    BvU

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    Yes, sorry: DCB

    Any results yet from the original poster ?
     
  15. Nov 6, 2014 #14
    I used the tangent-chord theorem to get the length of the chord. Since 2 tangent lines created the chord, it formed a triangle. The chord as the base and the radius as the legs. As shown at the attached picture.

    I used sine(45) to get the value of h. Sine 45 × 2 =h
    h = 1.41
    r - h = 2 - 1.41 = 0.59

    Using pythagorean theorem:
    2 = sqrt (X^2 + 0.59^2)
    X = 1.91 = Half of the chord

    2x = whole chord
    2 × 1.91 = 3.82

    Therefore, length of the chord is 3.82.

    Please cite your corrections. Thank you :)
     

    Attached Files:

  16. Nov 7, 2014 #15

    BvU

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    The 45 degrees is not correct. I don't understand the reasoning.

    "Draw AD, calculate |AD|, calculate |AB| .
    Look at isomorphic triangles ACE and DCB "

    What did you get for |AD|, |AB| ? Angle EAC ? Angle DCB ? Angle DBF ?
     
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