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**ENS 207 engineering graphics**

Lecture 3: Geometric constructions

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Points and Lines A point is used to represent a location in space but has no width, height, or depth. A line is used in drawings to represent the edge of a solid object.

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Angles An angle is formed by two intersecting lines. A common symbol for angle is Showing Angles

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**Geometric Constructions**

Triangles A triangle is a plane figure bounded by three straight sides. The sum of the interior angles is always 180º.

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**Geometric Constructions**

Circles and Arcs A circle is a closed curve, all points of which are the same distance from a point called the center.

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**Geometric Constructions**

Drawing an Arc Tangent to a Line and Through a Point with given radius Given line (AB), point (P), and radius (R) Draw line (DE) parallel to the given line (AB) at the distance (R) from it. From point (P) draw an arc with a radius (R) intersecting line (DE) at point (C). From point (C) draw the arc tangent to line (AB) and through point (P).

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**Drawing an arc tangent to a line or arc and through a point**

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**Geometric Constructions**

Drawing an Arc Tangent to Two Lines at Acute or Obtuse Angles Given two intersecting lines not making a 90º angle and the distance (R) Draw lines parallel to the given lines at a distance (R) from them to intersect at point (C). With (C) as the center and with the given radius (R) draw the required tangent arcs between the given lines.

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**Geometric Constructions**

Drawing an Arc Tangent an Arc and a Straight Line Given the straight line (AB) and the arc with radius (G) and the radius of desired arc (R) Draw a line parallel to the given lines at the distance (R). Draw an arc from center (O) with a radius equal to (G) plus (R) to intersect at (C). With (C) as the center and with the given radius (R) draw the required arc at the given radius (R) and tangent to the given line and arc.

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**Geometric Constructions**

Drawing an inside Arc Tangent to Two Arcs Given the two arcs with centers (A) and (B) and the radius of desired arc (R) With (A) and (B) as centers draw arcs parallel to the given arcs at the distance (R) from them to locate the intersection (C). With (C) as the center draw the required tangent arc at the given radius (R) to the given arcs.

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**Drawing an arc tangent to two arcs enclosing one or both**

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