It is easy to draw involutes to polygons. First, we have to point initial point and n extending sides. Then cutting extended lines with cumulative radiuses of length of sides gives points on involute and n joining m gives involute.

In logarithmic Spiral, values of vectorial angles are in arithmetical progression and radius vectors are in geometrical progression that is lengths of consecutive radius vectors enclosing equal angles are always constant.

A straight line parallel to asymptote intersects hyperbola at only one point. This says that part of hyperbola will lay in between parallel lines through outs its length after intersecting at one point.

For drawing perpendicular to a given line through a point that is outside line and is nearer to end of line we first cut an arc with radius equal to AD, keeping centre at A. n we draw anor arc with radius DP keeping centre at P. Then join both intersection points we get perpendicular.

Two circles can have two internally touching common tangents. Both tangents intersect at a point which is equidistant from centers of both circles. In or words, y intersect at a point which bisects line joining centers of circles.

If generating point is on circumference of generating circle n curve formed may be cycloids or hypocycloids. Trochoid is a curve generated by a point fixed to a circle, within or outside its circumference, as circle rolls along a straight line or a circle. But here given is outside so it is superior trochoid.

A regular polygon is a shape with 4 or more sides and all sides are of equal length. A regular polygon with five, six, seven, etc. sides are called as a regular pentagon, regular hexagon, regular heptagon, etc. respectively.

In second step in drawing arc of given radius touching two straight lines at right angles with each or, we draw anor arc from centre at new intersection of arc and lines and keeping radius same. The intersection of se two new arcs is centre of required arc.

Two tangents can be drawn from a point outside a given circle. The method to draw tangent to circle first involves joining point and centre and n drawing a semicircle with that length as diameter. Then join intersection points on circle and point outside you get tangent.

In general method of drawing an ellipse, if eccentricity of ellipse is given as 3/7 n line joining directrix and focus will have 10 divisions. The number is derived by adding numerator and denominator of eccentricity.