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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.

Correct Answer: ii, i, iv, iii
The normal to an involute of a circle is tangent to that circle. So simply by finding the appreciable tangent of circle passing through the point given on involute gives the normal and then by drawing perpendicular we can find the tangent to involute.

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 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 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 tangent to given circle and parallel to given line. Arrange the steps. i. Draw a perpendicular to given line and extend to cut the circle at two points P and Q. ii. At P or Q draw perpendicular to normal then we get the tangents. iii. PQ is the normal for required tangent. iv. Draw a circle with center O and line AB as required.

Given are the steps to draw a tangent to given circle from any point outside the circle. Arrange the steps. i. With OP as diameter, draw arcs on circle at R and R1. ii. Draw the given circle with center O. iii. Join P and R which is one tangent and PR1 is another tangent. iv. Mark the point P outside the circle.

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.

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 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.

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.