Article Index

B. Tangent line-arc intersection

The next two solutions deal with tangent a tangent line and arc.

1. Radius from line direction and radius point

Known information

  • Coordinates at point Q
  • Direction from point Q
  • Coordinates of radius point, point O

Determine

    • Radius of tangent arc
    • Coordinates of tangent point P

Figure I-2
Radius determination

Solution process

Inverse along the line from point Q to the radius point, O, to determine the direction and length of the line.

Compute angle Q as the difference between the directions AzQO and AzQP, subtracting the smaller from the larger, depending on which side of line QO line QP is.

Solve the following equations

Equation I-8
Equation I-9
Equation I-10
Equation I-11

2. Line direction from radius point and radius

Known information

  • Coordinates of radius point, point O
  • Arc radius
  • Coordinates of point Q

Determine

  • Direction of a line from point Q tangent to the arc; there are two possible directions, compute both
  • Coordinates of the two tangent points P1 and P2

Determine the direction of a line tangent to an arc.

Figure I-3
Tangent direction determination

Solution process

Inverse along the line from point point Q to the radius point O to determine its direction and length.

Compute angle g using Equation I-12.

Equation I-12

Angle g is used with the direction of line point Q to radius point O to determine the direction from point Q to each intersection point.

The distance from point Q to each intersection point is:

Equation I-13

To compute the coordinates of P1, perform a Forward Computation from point Q:

Equation I-13
Equation I-14
Equation I-15

To compute the coordinates of point P2, perform a Forward Computation from  point Q:

Equation I-16
Equation I-17
Equation I-18

 

Comments (0)

There are no comments posted here yet