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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.

Correct Answer: iv, iii, i, ii
It will take few simple steps to draw involute for a triangle since it has only 3 sides. 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 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.

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.

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.

Steps are given to find the normal and tangent to an epicycloid. Arrange the steps if C is the centre for generating circle and O is the centre of directing cycle. N is the point on epicycloid. i. Draw a line through O and D cutting directing circle at M. ii. Draw perpendicular to MN at N. We get tangent. iii. With centre N and radius equal to radius of generating circle, draw an arc cutting the locus of C at D. iv. Draw a line joining M and N which is normal.

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 determine the centre of curvature at a given point on a conic. Arrange the steps. Let P be the given point on the conic and F is the focus. Join P with F. Draw a line NR perpendicular to PN and cutting PF or PF-extended at R. Draw a line RO perpendicular to PR and cutting PN-extended at O which is centre of curvature. At P, draw a normal PN, cutting the axis at N.

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 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.