Get Advice on Live Video Call
Earn $ Cash $ with
consultations on Bissoy App

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.

Correct Answer: iv, ii, iii, i
The normal to an archemedian spiral at any point is the hypotenuse of the right angled triangle having the other two sides equal in length to the radius vector at that point and the constant of the curve respectively.

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 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 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.

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.

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 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 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.

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 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.