There are four basic types of intersections needed in surveying. They are bearing-bearing, distance-distance, bearing-distance and bearing-line.

Two lines, starting at different points and with different bearings, intersect at a single point. No intersection is computed if the lines are parallel.

Two circles, having different center or radius points, intersect at none, one (tangent circles) or two points. The circles may have different radii and may not intersect at all if one circle is inside the other or the distance between radius points is greater than the sum of their radii.

Each circle is defined by a center point and a distance for the radius.

A line and a circle intersect at none, one (tangent) or two points.

A center point (either Pt1 or Pt2) and a distance for the radius define the circle.

A line defined by a starting point and bearing/azimuth intersects the curve defined by two end points.

When computing a Bearing-Curve intersect, you can also tell TPC to allow intersections beyond the end points of the curve. By default, TPC only considers intersections between the end points of the curve.

- Choose COGO | Intersect to display the Intersect dialog.
- Enter the information you have for the intersection. If your intersection involves a
curve that is already defined in the survey, enter the endpoints of the
curve in the Point 2 and Point 3 fields. You can also use equations
to enter a distance or bearing/azimuth based on any points in the survey.
For example, to recall the bearing between points 12 and 24, enter “
**12..24**” in a Bearing field. - Enter any offset to create intersections parallel to the bearing you enter using negative for offset left and positive for offset right.
- Choose Save to save the computed points to the survey. They are not added to the survey when they are computed, only when you save them.
- To do another intersection, choose Clear.
- When you are finished creating intersection points, choose Close.

The Intersection dialog box will display only one valid intersection for a bearing-bearing intersection. It will display two valid intersections for a bearing-distance or distance-distance intersection. When TPC finds a valid intersection, one or both Computed Intersection fields will be available for entry (white rather than gray).

**Note**: Neither Computed Intersection field will be available if TPC can't find a
valid intersection based on the data you entered.

- Choose View. TPC will display the Point 1 line, the Point 2 line, and any computed intersection points. Use this information to decide which intersection point to save.

This example is a bearing-bearing intersection with offsets. The actual intersection point is offset to the left of the line from 1 to 2 and offset right of the line from 3 to 2

The offset distances specified do not have to be the same.

The intersection dialog box for this example would look like this, assuming an offset of 10 units to the left of the line from 1 to 2 and 12 units right of the line from 3 to 2.

The Bearing for Point 1 was derived from the equation 1..2 entered for this field. The Bearing for Point 2 was derived from the equation 3..2 entered for its field. Equations make it very easy to recall an azimuth, bearing or distance.

In this example, we want to find out where a line 10 units left of the property line from 1 to 2 intersects the curve from 5 to 1:1.

The intersection routine does not care if the curve is a tangent curve or not.

Now let’s look at the dialog box for this example. The rule for intersecting a bearing and a curve is that we enter the bearing information for Point 1 and use boxes on the right to define the curve.

Enter the starting point and bearing of the line in Point 1.

Now enter the end points of the cruve or press 'Or select a line >' and left click the curve in the current drawing.

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COGO Commands - reference