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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

Correct Answer: iv, iii, i, ii
Given here is the method for drawing regular polygons of a different number of sides of any length. This includes finding a line where all the centers for regular polygons lies and then with radius taking any end of 1st drawn line to center and then completing circle at last, cutting the circle with the same length of initial line. Thus we acquire polygons.

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

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 line. Arrange the steps. Let AB be the line and P be the point in it i. Join F and P which is perpendicular to AB. ii. Now C as centre take the same radius and cut the arc at D and again D as centre with same radius cut the arc further at E. iii. With centre as P take any radius and draw an arc (more than a semicircle) cuts AB at C. iv. Now D, E as centre take radius (more than half of DE) draw arcs which cut at F.

Arrange the following stages in a sequence, such that they result in an ogee curve between two parallel lines AB and CD, such that they are the tangents to the arc. m) Join the adjacent ends B and C with a straight line. n) Divide the line BC into four parts using the points P1, P2, P3. o) Draw lines such that they pass through the points P1, P2, P3, and are perpendicular to the line BC. p) Draw the perpendicular lines through the points B and C such that they cut the lines passing through P1, P3 respectively at E and F. q) With the center E draw an arc BP2 and with center F draw an arc P2C, thus arc BP2C is required ogee curve.

Given are the steps to draw a tangent to given arc even if center is unknown and the point P lies on it. Arrange the steps. Let AB be the arc. i. Draw EF, the bisector of the arc CD. It will pass through P. ii. RS is the required tangent. iii. With P as center and any radius draw arcs cutting arc AB at C and D. iv. Draw a perpendicular RS to EF through P.

Given are the steps to construct a square using a compass when the length of the side is given. Arrange the steps. i. Join A, B, C and D to form a square ii. At A with radius AB draw an arc, cut the AE at D iii. Draw a line AB with given length. At A draw a perpendicular AE to AB using arcs iv. With centers B and D and the same radius, draw arcs intersecting at C

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.

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.

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.

Steps are given to draw involute of given circle. Arrange the steps f C is the centre of circle and P be the end of the thread (starting point). i. Draw a line PQ, tangent to the circle and equal to the circumference of the circle. ii. Draw the involute through the points P1, P2, P3 ……..etc. iii. Divide PQ and the circle into 12 equal parts. iv. Draw tangents at points 1, 2, 3 etc. and mark on them points P1, P2, P3 etc. such that 1P1 =P1l, 2P2 = P2l, 3P3= P3l etc.

Given are the steps to draw a tangent to any given circle at any point P on it. Arrange the steps. i. Draw the given circle with center O and mark the point P anywhere on the circle. ii. With centers O and Q draw arcs with equal radius to cut each other at R. iii. Join R and P which is the required tangent. iv. Draw a line joining O and P. Extend the line to Q such that OP = PQ.