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The angle of the line is a degrees from North so the angle from East is (90 - a) degrees. Therefore gradient of the line is tan(90-a) = 1/tan(a).
Then any point on the line has coordinates (x, y) = (Lx + ksina, Ly + kcosa).
The coordinates of any point on the circle satisfy (x - Cx)2 + (y - Cy)2 = r2
The points of intersection must satisfy both equations so that:
(Lx + ksina - Cx)2 + (Ly + kcosa - Cy)2 = r2
This equation needs to be solved for k - everything else has a known numeric value. Since it is a quadratic, in k, there will be 0, 1 or 2 solutions for k depending on the line not intersecting the circle at all, being tangent to it and going through the circle.
The angle of the line is a degrees from North so the angle from East is (90 - a) degrees. Therefore gradient of the line is tan(90-a) = 1/tan(a).
Then any point on the line has coordinates (x, y) = (Lx + ksina, Ly + kcosa).
The coordinates of any point on the circle satisfy (x - Cx)2 + (y - Cy)2 = r2
The points of intersection must satisfy both equations so that:
(Lx + ksina - Cx)2 + (Ly + kcosa - Cy)2 = r2
This equation needs to be solved for k - everything else has a known numeric value. Since it is a quadratic, in k, there will be 0, 1 or 2 solutions for k depending on the line not intersecting the circle at all, being tangent to it and going through the circle.
The angle of the line is a degrees from North so the angle from East is (90 - a) degrees. Therefore gradient of the line is tan(90-a) = 1/tan(a).
Then any point on the line has coordinates (x, y) = (Lx + ksina, Ly + kcosa).
The coordinates of any point on the circle satisfy (x - Cx)2 + (y - Cy)2 = r2
The points of intersection must satisfy both equations so that:
(Lx + ksina - Cx)2 + (Ly + kcosa - Cy)2 = r2
This equation needs to be solved for k - everything else has a known numeric value. Since it is a quadratic, in k, there will be 0, 1 or 2 solutions for k depending on the line not intersecting the circle at all, being tangent to it and going through the circle.
The angle of the line is a degrees from North so the angle from East is (90 - a) degrees. Therefore gradient of the line is tan(90-a) = 1/tan(a).
Then any point on the line has coordinates (x, y) = (Lx + ksina, Ly + kcosa).
The coordinates of any point on the circle satisfy (x - Cx)2 + (y - Cy)2 = r2
The points of intersection must satisfy both equations so that:
(Lx + ksina - Cx)2 + (Ly + kcosa - Cy)2 = r2
This equation needs to be solved for k - everything else has a known numeric value. Since it is a quadratic, in k, there will be 0, 1 or 2 solutions for k depending on the line not intersecting the circle at all, being tangent to it and going through the circle.
What else can I help you with?
What is the intersection of the sphere with the yz plane?
The intersection of a sphere with a plane is a point, or a circle.
What is the intersection of 2 diameters of a circle called?
locus * * * * * A more likely answer is "the centre of the circle".
What is the maximum possible number of points of intersection between an equilateral triangle and a circle in the same plane?
6 maximum points of intersection
What is the place where a tangent line intersects a circle?
Definition: a tangent is a line that intersects a circle at exactly one point, the point of intersection is the point of contact or the point of tangency. a tangent is a line that intersects a circle at exactly one point, the point of intersection is the (point of contact) or the **point of tangency**.
What is produced by the intersection of a cone with a plane that is parallel to the base of the cone?
It is a circle - or at its extreme, a point.
What is the intersection of the sphere with the yz plane?
The intersection of a sphere with a plane is a point, or a circle.
What it the intersection of a line on a circle called?
The intersection of a line and a circle is called a chord if the line intersects the circle at two points. If the line touches the circle at exactly one point, it is referred to as a tangent. If the line does not intersect the circle at all, it is considered to be external to the circle.
What is the name of circle?
A circle is a type of conic section, produced by the intersection of a plane and a cone.
What is the intersection of 2 diameters of a circle called?
locus * * * * * A more likely answer is "the centre of the circle".
When a plane intersects a sphere what does the intersection form?
A circle~
What point of intersection is the center of a circumscribed circle?
circumcenter
How do you find the center of a circle?
it is the intersection of the medians of two cords!
Pi can be used to calculate the blank of a circle?
Pi can be used to calculate the area of a circle Pi can be used to calculate the circumference of a circle
If you have a circle and a square what is the maximum number of points of intersection that the shapes can share?
If the circle is inside the square, four.
What is the point of intersection of a circle of a sphere with tangent line or plane?
The point of intersection of a tangent line or plane with a circle on a sphere is the single point where the line or plane touches the circle. This point is unique because, by definition, a tangent line or plane only intersects a circle at one point without passing through it. If the tangent is from an external point, it signifies that the line or plane is just "touching" the circle at that specific location. In three-dimensional space, this concept illustrates the relationship between the geometry of the sphere and the properties of tangents.
Intersection of sphere and plane that contains center of a sphere?
great circle
What type of geometric figure is formed by the intersection of a plane and sphere?
A Circle.
