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originally posted by: iowaporter
...With the right triangle, you can use:
Sin = Opposite/Hypotenuse ...
originally posted by: iowaporter
a reply to: iowaporter
Finally, since the poster probably intends the blue line to vary in length and always be tangent to the bubble.
Then the above angles between the blue and yellow lines are 30, 45, and 90 degrees.
Then the X,Y coordinates would be:
Radius .5, Angle 30, Coordinates (-.25, .43)
Radius .707, Angle 45, Coordinates (-.5, .5)
Radius 1, Angle 90, Coordinates (-1, 0)
Once we form the right triangle between the yellow line (H) and blue line (A) and the radius of the bubble (O) and then calculate the angle between the blue and yellow lines, we can calculate the third angle of the right triangle. In the first case, 180 - 90 - 30 = 60. Then we subtract that from 180 to get the angle from the positive X axis. Then, for a unit circle, we know that Cos(theta) = X and Sin(theta) = Y.
BUT - since the bubble isn't a unit circle until the radius is 1, we have the multiply the resulting coordinates by the actual radius.
So, when the angle between the blue and yellow lines is 45, the opposite angle is also 45 (135 when measuring from the positive x axis) and the X and Y coordinates would be (-.707, .707) for a unit circle. But, since the radius is .707, we have to multiply that times the results to get the final coordinates of (.5, .5).
originally posted by: iowaporter
a reply to: Soylent Green Is People
But if we define the blue line as a line with a fixed point on the outer circle and tangent to the bubble, then a real line does exist at that point and tangent to the bubble. The angle between the blue and yellow lines is 90. And the X and Y coordinates of that point are -1 and 0.
originally posted by: iowaporter
a reply to: Soylent Green Is People
By definition, a line is always infinite. On that line, there is a line SEGMENT with endpoints on the large circle and the bubble. The picture illustrates the segment, but the description describes the line.