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# Geometry for Modeling and Design

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## 4.3 Drawing an Arc Tangent to a Line or Arc and Through a Point

Given line AB, point P, and radius R (Figure 4.25a), draw line DE parallel to the given line and distance R from it. From P draw an arc with radius R, cutting line DE at C, the center of the required tangent arc. 4.25 Tangents. These are often easy constructions using CAD and object snaps.

Given line AB, with tangent point Q on the line and point P (Figure 4.25b), draw PQ, which will be a chord of the required arc. Draw perpendicular bisector DE, and at Q draw a line perpendicular to the line to intersect DE at C, the center of the required tangent arc.

Given an arc with center Q, point P, and radius R (Figure 4.25c), from P, draw an arc with radius R. From Q, draw an arc with radius equal to that of the given arc plus R. The intersection C of the arcs is the center of the required tangent arc.