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ASSIGNMENT NO 1, , DRAW THE FOLLOWING GEOMETRICAL, CONSTRUCTIONS (Assume suitable dimensions, wherever necessary), , 1. 15° lines, 120° lines, 135° lines (5 each) to the, given base line of 60mm using set squares, , 2 A square of side 40 mm using a protractor/chop, 3.1 Divide a given circle in 5 equal parts & draw a, pentagon using protractor/chop ( Fig. 5.48 ), , 3.2 Divide a given circle in 7 equal parts & draw a, heptagon in it. (Fig. 5.50), , 4.1 Bisect a line of 60 mm 4 equal parts (15 mm, apart), , 4.2 Bisect an angle of 50°, , 5.1 Draw tangent to the given circle (Fig. 5.57), 5.2 A tangent to the given are. (Fig. 5.59), , 6 Inscribe a circle in given equilateral triangle of, 50mm. (Fig 5.73), , 7. Will give later

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Art, 5-14] Geometrical Construction 87, , Problem 5-32. To inscribe a repular pentagon ina given circle (fig, 5-48),, (i) With centre O, draw the given circle,, (ii), Draw diameters AB and CD perpendicul, , (iii) Bisect AO in a point P. With centre P and radius PC, draw an arc cutting OB, in Q., , ar to each other,, , (iv) With centre C and radius CQ, draw, , (v) With centres £ and F and the same, and H respectively,, , (vi) Draw lines CE, EG, GH, HF and FC, thus completing the re, , an are cutting the circle in £ and F., , radius, draw arcs cutting the circle in G, , quired pentagon., , , , Fic. 5-48 Fic. 5-49, , Problem 5-33. To inscribe a regular hexagon in a given circle (fig. 5-49)., Apply the same method as shown in Problem 5-28(b)., , Note: (a) When two sides of the hexagon are required to be horizontal the starting point, for stepping-off equal divisions should be on an end of the horizontal diameter., , (b) If they are to be vertical, the starting point should be on an end of the vertical, diameter., , In either case, to avoid inaccuracy, the points should be joined with the aid of, T-square and 30°-60° set-square., , Problem 5-34. To inscribe a regular heptagon in a, given circle (fig. 5-50)., (i) With centre O, draw the given circle., , (ii), Draw a diameter AB. With centre A and radius, AO, draw an arc cutting the circle at E and F., , (iii) Draw a line EF, cutting AO in G,, Then EG or FG is the length of the side of the, heptagon., , Therefore, from any point on the circle, say A, step-off, divisions equal to EG, around the circle. Join the, division-points and obtain the heptagon.

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5-16., , TO DRAW TANGENTS, , Problem 5-40. (fig. 5-57): To draw a tangent to, , a given, , (i), , (ii), (iii), (iv), , circle at any point on it., , With centre O, draw the given circle and mark, a point P on it., , Draw a line joining O and P., Produce OP to Q so that PQ = OP., , With centres O and Q and with any convenient, radius, draw arcs intersecting each other at R., , Draw a line through P and R. Then this, line is the required tangent., , FIG. 5-57

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90 Engineering Drawing, , Problem 5-42. (fig. 5-59): To draw a tangent, to a given arc of inaccessible centre at any point, on it., , Let AB be the given arc and P the point on it., , (i) With centre P and any radius, draw arcs cutting, , the arc AB at C and D. Draw EF, the bisector, of the arc CD. It will pass through P., , (ii) Through P, draw a line RS perpendicular to EF., RS is the required tangent., , , , Fic. 5-59

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Problem 5-54. To inscribe a circle in given, triangle (fig. 5-73)., Let ABC be the triangle., , (i) Bisect any two angles by lines intersecting, each other at O., , (ii) Draw a perpendicular from O to any one, side of the triangle, meeting it at P. <i A, (iii) With centre O and radius OP, describe cs. ~~, the required circle. 3 P, IG. 5-73