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# Geometry for Modeling and Design

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## Chapter Exercises

Exercise 4.1 Draw inclined line AB 65 mm long. Bisect it with line CD.

Exercise 4.2 Draw any angle. Label its vertex C. Bisect the angle and transfer half the angle to place its vertex at arbitrary point D.

Exercise 4.3 Draw an inclined line EF. Use distance GH equal to 42 mm. Draw a new line parallel to EF and distance GH away.

Exercise 4.4 Draw line JK 95 mm long. Draw a second line LM 58 mm long. Divide JK into five equal parts. Use a different method than you selected to divide line JK to divide line LM into three equal parts.

Exercise 4.5 Draw line OP 92 mm long. Divide it into three proportional parts with the ratio 3:5:9.

Exercise 4.6 Draw a line 87 mm long. Divide it into parts proportional to the square of x, where x = 1, 2, 3, and 4.

Exercise 4.7 Draw a triangle with the sides 76 mm, 85 mm, and 65 mm. Bisect the three interior angles. The bisectors should meet at a point. Draw a circle inscribed in the triangle, with the point where the bisectors meet as its center.

Exercise 4.8 Draw a right triangle that has a hypotenuse of 65 mm and one leg 40 mm. Draw a circle through the three vertices.

Exercise 4.9 Draw inclined line QR 84 mm long. Mark point P on the line 32 mm from Q. Draw a line perpendicular to QR at point P. Select any point S 45.5 mm from line QR. Draw a line perpendicular from S to line QR.

Exercise 4.10 Draw two lines forming an angle of 35.5°.

Exercise 4.11 Draw two lines forming an angle of 33.16°.

Exercise 4.12 Draw an equilateral triangle with sides of 63.5 mm. Bisect the interior angles. Draw a circle inscribed in the triangle.

Exercise 4.13 Draw an inclined line TJ 55 mm long. Using line TJ as one of the sides, construct a square.

Exercise 4.14 Create a 54-mm-diameter circle. Inscribe a square in the circle, and circumscribe a square around the circle.

Exercise 4.15 Create a 65-mm-diameter circle. Find the vertices of an inscribed regular pentagon. Join these vertices to form a five-pointed star.

Exercise 4.16 Create a 65-mm-diameter circle. Inscribe a hexagon, and circumscribe a hexagon.

Exercise 4.17 Create a square with 63.5 mm sides. Inscribe an octagon.

Exercise 4.18 Draw a triangle with sides 50 mm, 38 mm, and 73 mm. Copy the triangle to a new location and rotate it 180°.

Exercise 4.19 Make a rectangle 88 mm wide and 61 mm high. Scale copies of this rectangle, first to 70 mm wide and then to 58 mm wide.

Exercise 4.20 Draw three points spaced apart randomly. Create a circle through the three points.

Exercise 4.21 Draw a 58-mm-diameter circle. From any point S on the left side of the circle, draw a line tangent to the circle at point S. Create a point T, to the right of the circle and 50 mm from its center. Draw two tangents to the circle from point T.

Exercise 4.22 Open-Belt Tangents. Draw a horizontal centerline near the center of the drawing area. On this centerline, draw two circles spaced 54 mm apart, one with a diameter of 50 mm, the other with a diameter of 38 mm. Draw “open-belt”-style tangents to the circles.

Exercise 4.23 Crossed-Belt Tangents. Use the same instructions as Exercise 4.22, but for “crossed-belt”-style tangents.

Exercise 4.24 Draw a vertical line VW. Mark point P 44 mm to the right of line VW. Draw a 56-mm-diameter circle through point P and tangent to line VW.

Exercise 4.25 Draw a vertical line XY. Mark point P 44 mm to the right of line XY. Mark point Q on line XY and 50 mm from P. Draw a circle through P and tangent to XY at point Q.

Exercise 4.26 Draw a 64-mm-diameter circle with center C. Create point P to the lower right and 60 mm from C. Draw a 25-mm-radius arc through P and tangent to the circle.

Exercise 4.27 Draw intersecting vertical and horizontal lines, each 65 mm long. Draw a 38-mm-radius arc tangent to the two lines.

Exercise 4.28 Draw a horizontal line. Create a point on the line. Through this point, draw a line upward to the right at 60° from horizontal. Draw 35-mm-radius arcs in an obtuse and an acute angle tangent to the two lines.

Exercise 4.29 Draw two intersecting lines to form a 60° angle. Create point P on one line a distance of 45 mm from the intersection. Draw an arc tangent to both lines with one point of tangency at P.

Exercise 4.30 Draw a vertical line AB. In the lower right of the drawing, create a 42-mm-radius arc with its center 75 mm to the right of the line. Draw a 25-mm-radius arc tangent to the first arc and to line AB.

Exercise 4.31 With centers 86 mm apart, draw arcs of radii 44 mm and 24 mm. Draw a 32-mm-radius arc tangent to the two arcs.

Exercise 4.32 Draw a horizontal centerline near the center of the drawing area. On this centerline, draw two circles spaced 54 mm apart, one with a diameter of 50 mm, the other with a diameter of 38 mm. Draw a 50-mm-radius arc tangent to the circles and enclosing only the smaller one.

Exercise 4.33 Draw two parallel inclined lines 45 mm apart. Mark a point on each line. Connect the two points with an ogee curve tangent to the two parallel lines. (An ogee curve is a curve tangent to both lines.)

Exercise 4.34 Draw a 54-mm-radius arc that subtends an angle of 90°. Find the length of the arc.

Exercise 4.35 Draw a horizontal major axis 10 mm long and a minor axis 64 mm long to intersect near the center of the drawing space. Draw an ellipse using these axes.

Exercise 4.36 Create six equal rectangles and draw visible lines, as shown. Omit dimensions and instructional notes.

Exercise 4.37 Create six equal rectangles and draw lines as shown. In the first two spaces, draw examples of the standard line patterns used in technical drawings: visible, hidden, construction, centerlines, cutting-plane lines, and phantom. In the remaining spaces, locate centers C by diagonals, and then work constructions out from them. Omit the metric dimensions and instructional notes.

Exercise 4.38 Draw the figures as shown. Omit all dimensions.

Exercise 4.39 Draw the friction plate. Omit dimensions and notes.

Exercise 4.40 Draw the Geneva cam. Omit dimensions and notes.

Exercise 4.41 Draw accurately in pencil the shear plate. Give the length of KA. Omit the other dimensions and notes.

Exercise 4.42 Draw the ratchet wheel using pencil. Omit the dimensions and notes.

Exercise 4.43 Draw the latch plate using pencil. Omit the dimensions and notes.

Exercise 4.44 Draw the parabolic floodlight reflector shown.

Exercise 4.45 Identify the solid primitives and Boolean operations you could use to create the following objects.

Exercise 4.46 Use an isometric grid to help sketch the solids formed by revolving the following shapes about the axis shown. Coordinates are defined by the X-Y-Z icon, with positive X to the right, positive Y up, and positive Z out of the page.

Exercise 4.47 Use an isometric grid to help sketch the solids formed by extruding the following shapes along the axis specified. Coordinates are defined by the X-Y-Z icon, with positive X to the right, positive Y up, and positive Z out of the page.

Exercise 4.48 Starting at point A in each of the figures, list the coordinates for each point in order as relative coordinates from the previous point.

Exercise 4.49 Plot the coordinates in each of the lists on grid paper. Each point represents the endpoint of a line from the previous point, unless otherwise indicated. Relative coordinates are preceded by @.

Exercise 4.50 Using the information provided on the drawing, determine the coordinates you would use (absolute, relative, or polar) and the order in which you would enter them to create the figure.

Exercise 4.51 Using the information provided on the drawing, determine the coordinates you would use (absolute, relative, or polar) and the order in which you would enter them to create the figure.

Exercise 4.52 Using the information provided on the drawing, determine the coordinates you would use (absolute, relative, or polar) and the order in which you would enter them to create the figure.