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Given are the steps to draw a perpendicular to a line from a point outside the line, when the point is nearer the centre of line. Arrange the steps. Let AB be the line and P be the point outside the line i. Take P as centre and take some convenient radius draw arcs which cut AB at C, D. ii. Join E, F and extend it, which is perpendicular to AB. iii. From C, D with radius R1 (more than half of CD), draw arcs which cut each other at E. iv. Again from C, D with radius R2 (more than R1), draw arcs which cut each other at F.
Given are the steps to draw a perpendicular to a line from a point outside the line, when the point is near the centre of line. Arrange the steps. Let AB be the line and P be the point outside the line i. The line EP is perpendicular to AB ii. From P take convenient radius and draw arcs which cut AB at two places, say C, D. iii. Join E and P. iv. Now from centers C, D draw arc with radius (more than half of CD), which cut each other at E.
Steps are given to draw normal and tangent to an archemedian curve. Arrange the steps, if O is the center of curve and N is point on it. i. Through N, draw a line ST perpendicular to NM. ST is the tangent to the spiral. ii. Draw a line OM equal in length to the constant of the curve and perpendicular to NO. iii. Draw the line NM which is normal to the spiral. iv. Draw a line passing through the N and O which is radius vector.
Given are the steps to draw a perpendicular to a line from a point outside the line, when the point is near an end of the line. Arrange the steps. Let AB be the line and P be the point outside the line i. The line ED is perpendicular to AB ii. Now take C as centre and CP as radius cut the previous arc at two points say D, E. iii. Join E and D. iv. Take A as center and radius AP draw an arc (semicircle), which cuts AB or extended AB at C.
Steps are given to find the normal and tangent for a cycloid. Arrange the steps if C is the centre for generating circle and PA is the directing line. N is the point on cycloid. i. Through M, draw a line MO perpendicular to the directing line PA and cutting at O. ii. With centre N and radius equal to radius of generating circle, draw an arc cutting locus of C at M. iii. Draw a perpendicular to ON at N which is tangent. iv. Draw a line joining O and N which is normal.
Steps are given to draw tangent and normal to the involute of a circle (center is C) at a point N on it. Arrange the steps. i. With CN as diameter describe a semi-circle cutting the circle at M. ii. Draw a line joining C and N. iii. Draw a line perpendicular to NM and passing through N which is tangent. iv. Draw a line through N and M. This line is normal.
Given are the steps to construct regular polygon of any number of sides. Arrange the steps. i. Draw the perpendicular bisector of AB to cut the line AP in 4 and the arc AP in 6 ii. The midpoint of 4 and 6 gives 5 and extension of that line along the equidistant points 7, 8, etc gives the centers for different polygons with that number of sides and the radius is AN (N is from 4, 5, 6, 7, so on to N) iii. Join A and P. With center B and radius AB, draw the quadrant AP iv. Draw a line AB of given length. At B, draw a line BP perpendicular and equal to AB
Given are the steps to draw a perpendicular to a line at a point within the line when the point is near the centre of a line. Arrange the steps. Let AB be the line and P be the point in it i. P as centre, take convenient radius R1 and draw arcs on the two sides of P on the line at C, D. ii. Join E and P iii. The line EP is perpendicular to AB iv. Then from C, D as centre, take R2 radius (greater than R1), draw arcs which cut at E.
Arrange the steps. These give procedure to draw internal tangent to two given circles of equal radii. i. Draw a line AB which is the required tangent. ii. Draw the given circles with centers O and P. iii. With center R and radius RA, draw an arc to intersect the other circle on the other circle on the other side of OP at B. iv. Bisect OP in R. Draw a semi circle with OR as diameter to cut the circle at A.
Given are the steps to construct an equilateral triangle, with help of a compass, when the length of altitude is given. Arrange the steps. i. Draw a line AB of any length. At any point P on AB, draw a perpendicular PQ equal to altitude length given ii. Draw bisectors of CE and CF to intersect AB at R and T respectively.QRT is required triangle iii. With center Q and any radius, draw an arc intersecting PQ at C iv. With center C and the same radius, draw arcs cutting the 1st arc at E and F