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Steps given are to draw an involute of a given square ABCD. Arrange the steps. i. With B as centre and radius BP1 (BA+ AD) draw an arc to cut the line CB-produced at P2. ii. The curve thus obtained is the involute of the square. iii. With centre A and radius AD, draw an arc to cut the line BA-produced at a point P1. iv. Similarly, with centres C and D and radii CP2 and DP3 respectively, draw arcs to cut DC-produced at P3 and AD-produced at P4.

Correct Answer: iii, i , iv, ii
It is easy to draw involutes to polygons. First, we have to point the initial point and then extending the sides. Then cutting the extended lines with cumulative radiuses of length of sides gives the points on involute and then joining them gives involute.

Steps given are to draw an involute of a given pentagon ABCDE. Arrange the steps. i. B as centre and radius AB, draw an arc cutting BC –extended at 1. ii. The curve thus obtained is the involute of the pentagon. iii. C as centre and radius C1, draw an arc cutting CD extended at 2. iv. Similarly, D, E, A as centres and radius D2, E3, A4, draw arcs cutting DE, EA, AB at 3, 4, 5 respectively.

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.

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 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.

Steps given are to draw an involute of a given triangle ABC. Arrange the steps. i. With C as centre and radius C1 draw arc cutting AC-extended at 2. ii. With A as center and radius A2 draw an arc cutting BA- extended at 3 completing involute. iii. B as centre with radius AB draw an arc cutting the BC- extended at 1. iv. Draw the given triangle with corners A, B, 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 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 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

Steps are given to draw the evolute of a hypocycloid. Arrange the steps. i. Draw the diameter PQ of the rolling circle. Join Q with O, the centre of the directing circle. ii. Mark a number of points on the hypocycloid and similarly, obtain centres of curvature at these points. The curve drawn through these centres is the evolute of the hypocycloid. iii. Produce PN to cut OQ- produced at Op, which is the centre of curvature at the point P. iv. Mark a point P on the hypocycloid and draw the normal PN to it.

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.