Article Index

D. Examples

1. Three point curve

Three known coordinate points are

Point North (ft) East (ft)
A 902.72 1751.91
B 870.76 1237.76
C 538.57 1293.16

Determine the radius of the circle passing through the points and coordinates of the radius point.

Sketch

Compute the coefficients using Equations I-3 through I-6

Use the coefficients in Equations I-1 and I-2 to get radius point coordinates

Get radius from Equation I-7

Using point A

Check using point B

Checks within rounding.

Answers

Radius   294.42'
Radius pt coords   744.39' N
    1503.68' E

2. Tangent line

What is the direction of the line line tangent to the arc shown below? What are the coordinates of the intersection point?

Inverse from point W to the radius point O

Using Equation I-12 compute the angle g between the line to the radius point and tangent line.

Determine the azimuth and length of the tangent line

.

Since the tangent line is left of the line to the radius point, to get its azimuth subtract g from AzWO' Equation, I-16.

Its length comes from Equation I-13

Forward Computation, Equations I-17 and I-18, to compute tangent point coordinates

Answers

Tangent azimuth   72°45'42"
Tangent pt coords   1501.00' N
    1810.34' E

3. Three-tangent arc

What is the radius of the arc that is tangent to the three line shown?

Label the geometry

Establsh points G and H using direction-direction intersections (results shown, comps left to user)

Point North East
G 1849.672 1305.139
H 1735.850 1670.923

ΔG and ΔH from the azimuths (comps left to user)

ΔG 63°05'03"
ΔH 49°03'40"

Inverse Computation to obtain distance from point G to point H  (comps left to user): 383.084

Apply Equation I-19 to get the arc radius

Tangent distance for first arc section (comps left to user): 219.721

Radius point coordinates (comps left to user): 1,442.592' N and 1,408.580' E

Answers

Radius   357.96'
Radius pt coords   1,442.59' N
    1,408.58' E

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