### 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  Using point A Check using point B Checks within rounding.

#### 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 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