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Math Help - Where the line intersects the circle

  1. #1
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    Where the line intersects the circle

    Prologue:
    I am a graphic designer who often creates her own scripts to help with the process. So, I'm not a high-school student. It's been over 20 years since high school geometry (I'm deliberately not counting - I don't want to know). Anyway, I hope one of you wizards will take pity on me dispite my non-student & non-teacher status...

    Problem:
    I'm attempting to calculate the x,y coordinate of a point along a circle at a given angle. (it happens to be the point at which a line radiates from the center of the circle outward). I know the radius of the circle & the center points. I know the angle.

    Possibilities:
    I tried to take the equation of a circle (x + h)^2 +(y+k)^2=r^2 & plug in the equation of the line y = mx + b but my brain fused. Ouch. Any suggestions?

    Thank you,
    Mae
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  2. #2
    MHF Contributor
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    Apr 2008
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    1,092
    If you were going to take the approach that you mentioned, a small nitpick: The equation of the circle is (x - h)^2 + (y - k)^2 = r^2. However, there is an easier method. Let the center of the circle be (h, k), and the radius be r. Then:

    x = h + r \cos(\theta)
    y = k + r \sin(\theta)

    where the angle \theta is measured from the positive x-axis moving counterclockwise.
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  3. #3
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    Sep 2008
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    Right, derived from the old c^2=a^2+b^2.

    Many thanks.

    Mae
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