I shall make it a little more clear. Let's say x is a point on the diameter which is at a distance a from the center point. Then how do you find out the distance from x to various points on the circumference of the circle. Is there any equation which satisfies it or how do we get a set of values 'y' that gets all the distances from x to the circumference. It would be great if someone would explain it to me bcos I have been whacking my brain with no solutions!
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the distance from the center of the circle to the point x is (a).
if you draw the perpendicular to the diameter through x, it will intersect the circle at two points.
if you draw the radius from the center to each of the two intersection points, you will get two right triangles.
and you know how to deal with right triangles -- e.g. pythagoras gives you the length of the vertical from x to the circle. [= sqrt( R^2 - a^2 ); where R is the radius of the circle.]
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choose a point (y) on the circumference.
the trick is that you have to specify (y) somehow: one way is to specify the (x,y) coordinate.
another way is to specify the mathematical angle from the x-axis to you have to rotate through to reach (y).
these two methods of identification are transitive because you know
x = R cos(t)
y = R sin(t)
where (x,y) is the location of (y) and t is the angle traversed to reach (y) from the x-axis.
at that point, you can draw the radius from center to (y), and now you have two legs [ (a) and R ] and the angle between them [ pi - t ].
at that point, you can use trigonometry to get the length of the remaining leg, which is the distance from (x) to (y)
if you draw the perpendicular to the diameter through x, it will intersect the circle at two points.
if you draw the radius from the center to each of the two intersection points, you will get two right triangles.
and you know how to deal with right triangles -- e.g. pythagoras gives you the length of the vertical from x to the circle. [= sqrt( R^2 - a^2 ); where R is the radius of the circle.]
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choose a point (y) on the circumference.
the trick is that you have to specify (y) somehow: one way is to specify the (x,y) coordinate.
another way is to specify the mathematical angle from the x-axis to you have to rotate through to reach (y).
these two methods of identification are transitive because you know
x = R cos(t)
y = R sin(t)
where (x,y) is the location of (y) and t is the angle traversed to reach (y) from the x-axis.
at that point, you can draw the radius from center to (y), and now you have two legs [ (a) and R ] and the angle between them [ pi - t ].
at that point, you can use trigonometry to get the length of the remaining leg, which is the distance from (x) to (y)
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I'd use a ruler.